Ideal of matrix ring
I'm going over some exercises and I'm not quite sure if I completely understand this one.
Let $R=M_3(mathbb{Q})$, i.e. $R$ is the ring of all $3times3$ matrices over rational numbers. Describe the minimal right ideal of $R$ containing the matrix
$$begin{bmatrix}
1 & 0 & 1 \
1 & 1 & 0 \
0 & 1 & 1 \
end{bmatrix}$$
M̶y̶ ̶g̶u̶e̶s̶s̶ ̶w̶a̶s̶ ̶t̶h̶a̶t̶ ̶I̶'̶m̶ ̶j̶u̶s̶t̶ ̶s̶u̶p̶p̶o̶s̶e̶d̶ ̶t̶o̶ ̶f̶i̶n̶d̶ ̶a̶ ̶m̶a̶t̶r̶i̶x̶ ̶i̶ ̶t̶h̶a̶t̶ ̶f̶i̶t̶s̶ ̶t̶h̶e̶ ̶d̶e̶f̶i̶n̶i̶t̶i̶o̶n̶ ̶o̶f̶ ̶a̶ ̶r̶i̶g̶h̶t̶ ̶i̶d̶e̶a̶l̶,̶ ̶w̶h̶i̶c̶h̶ ̶i̶s̶ ̶∀̶ ̶r̶ ̶∈̶ ̶R̶:̶ ̶i̶ ̶·̶ ̶r̶ ̶∈̶ ̶I̶ ̶(̶r̶ ̶b̶e̶i̶n̶g̶ ̶t̶h̶e̶ ̶g̶i̶v̶e̶n̶ ̶m̶a̶t̶r̶i̶x̶)̶ ̶a̶n̶d̶ ̶I̶ ̶=̶ ̶{̶(̶i̶)̶}̶ ̶.̶
But the more I tried to find something similar to this problem, the more I think that this is absolutely wrong. Can somebody help me with this and maybe explain how to get to the solution?
Thank you!
EDIT
My previous idea was a mix up of definitions, from the comments I now understand that I need to find $I$ (which contains the given matrix), but I'm still confused as to how to do so.
abstract-algebra matrices ring-theory ideals
asked Jan 4 at 21:20
AlexAlex
304
New contributor
Alex is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
I'm going over some exercises and I'm not quite sure if I completely understand this one.
Let $R=M_3(mathbb{Q})$, i.e. $R$ is the ring of all $3times3$ matrices over rational numbers. Describe the minimal right ideal of $R$ containing the matrix
$$begin{bmatrix}
1 & 0 & 1 \
1 & 1 & 0 \
0 & 1 & 1 \
end{bmatrix}$$
M̶y̶ ̶g̶u̶e̶s̶s̶ ̶w̶a̶s̶ ̶t̶h̶a̶t̶ ̶I̶'̶m̶ ̶j̶u̶s̶t̶ ̶s̶u̶p̶p̶o̶s̶e̶d̶ ̶t̶o̶ ̶f̶i̶n̶d̶ ̶a̶ ̶m̶a̶t̶r̶i̶x̶ ̶i̶ ̶t̶h̶a̶t̶ ̶f̶i̶t̶s̶ ̶t̶h̶e̶ ̶d̶e̶f̶i̶n̶i̶t̶i̶o̶n̶ ̶o̶f̶ ̶a̶ ̶r̶i̶g̶h̶t̶ ̶i̶d̶e̶a̶l̶,̶ ̶w̶h̶i̶c̶h̶ ̶i̶s̶ ̶∀̶ ̶r̶ ̶∈̶ ̶R̶:̶ ̶i̶ ̶·̶ ̶r̶ ̶∈̶ ̶I̶ ̶(̶r̶ ̶b̶e̶i̶n̶g̶ ̶t̶h̶e̶ ̶g̶i̶v̶e̶n̶ ̶m̶a̶t̶r̶i̶x̶)̶ ̶a̶n̶d̶ ̶I̶ ̶=̶ ̶{̶(̶i̶)̶}̶ ̶.̶
But the more I tried to find something similar to this problem, the more I think that this is absolutely wrong. Can somebody help me with this and maybe explain how to get to the solution?
Thank you!
EDIT
My previous idea was a mix up of definitions, from the comments I now understand that I need to find $I$ (which contains the given matrix), but I'm still confused as to how to do so.
abstract-algebra matrices ring-theory ideals
asked Jan 4 at 21:20
AlexAlex
304
New contributor
Alex is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
3
Ideals are not matrices! Ideals are sets of matrices. You need to find the smallest $I subseteq R$ such that $left(array{1&0&1\1&1&0\0&1&1}right)in I$ and for any $r in R$ and any $i in I$, $ir in I$.
– user3482749
Jan 4 at 21:26
I second what @user3482749 said. It seems that you don't quite understand the definition of ideals, so you need to go back and read it more carefully. What you stated as a "definition" has bits and pieces of the correct one, but the way it's stated doesn't make much sense...
– zipirovich
Jan 4 at 22:25
add a comment |
I'm going over some exercises and I'm not quite sure if I completely understand this one.
Let $R=M_3(mathbb{Q})$, i.e. $R$ is the ring of all $3times3$ matrices over rational numbers. Describe the minimal right ideal of $R$ containing the matrix
$$begin{bmatrix}
1 & 0 & 1 \
1 & 1 & 0 \
0 & 1 & 1 \
end{bmatrix}$$
M̶y̶ ̶g̶u̶e̶s̶s̶ ̶w̶a̶s̶ ̶t̶h̶a̶t̶ ̶I̶'̶m̶ ̶j̶u̶s̶t̶ ̶s̶u̶p̶p̶o̶s̶e̶d̶ ̶t̶o̶ ̶f̶i̶n̶d̶ ̶a̶ ̶m̶a̶t̶r̶i̶x̶ ̶i̶ ̶t̶h̶a̶t̶ ̶f̶i̶t̶s̶ ̶t̶h̶e̶ ̶d̶e̶f̶i̶n̶i̶t̶i̶o̶n̶ ̶o̶f̶ ̶a̶ ̶r̶i̶g̶h̶t̶ ̶i̶d̶e̶a̶l̶,̶ ̶w̶h̶i̶c̶h̶ ̶i̶s̶ ̶∀̶ ̶r̶ ̶∈̶ ̶R̶:̶ ̶i̶ ̶·̶ ̶r̶ ̶∈̶ ̶I̶ ̶(̶r̶ ̶b̶e̶i̶n̶g̶ ̶t̶h̶e̶ ̶g̶i̶v̶e̶n̶ ̶m̶a̶t̶r̶i̶x̶)̶ ̶a̶n̶d̶ ̶I̶ ̶=̶ ̶{̶(̶i̶)̶}̶ ̶.̶
But the more I tried to find something similar to this problem, the more I think that this is absolutely wrong. Can somebody help me with this and maybe explain how to get to the solution?
Thank you!
EDIT
My previous idea was a mix up of definitions, from the comments I now understand that I need to find $I$ (which contains the given matrix), but I'm still confused as to how to do so.
abstract-algebra matrices ring-theory ideals
asked Jan 4 at 21:20
AlexAlex
304
New contributor
Alex is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I'm going over some exercises and I'm not quite sure if I completely understand this one.
Let $R=M_3(mathbb{Q})$, i.e. $R$ is the ring of all $3times3$ matrices over rational numbers. Describe the minimal right ideal of $R$ containing the matrix
$$begin{bmatrix}
1 & 0 & 1 \
1 & 1 & 0 \
0 & 1 & 1 \
end{bmatrix}$$
M̶y̶ ̶g̶u̶e̶s̶s̶ ̶w̶a̶s̶ ̶t̶h̶a̶t̶ ̶I̶'̶m̶ ̶j̶u̶s̶t̶ ̶s̶u̶p̶p̶o̶s̶e̶d̶ ̶t̶o̶ ̶f̶i̶n̶d̶ ̶a̶ ̶m̶a̶t̶r̶i̶x̶ ̶i̶ ̶t̶h̶a̶t̶ ̶f̶i̶t̶s̶ ̶t̶h̶e̶ ̶d̶e̶f̶i̶n̶i̶t̶i̶o̶n̶ ̶o̶f̶ ̶a̶ ̶r̶i̶g̶h̶t̶ ̶i̶d̶e̶a̶l̶,̶ ̶w̶h̶i̶c̶h̶ ̶i̶s̶ ̶∀̶ ̶r̶ ̶∈̶ ̶R̶:̶ ̶i̶ ̶·̶ ̶r̶ ̶∈̶ ̶I̶ ̶(̶r̶ ̶b̶e̶i̶n̶g̶ ̶t̶h̶e̶ ̶g̶i̶v̶e̶n̶ ̶m̶a̶t̶r̶i̶x̶)̶ ̶a̶n̶d̶ ̶I̶ ̶=̶ ̶{̶(̶i̶)̶}̶ ̶.̶
But the more I tried to find something similar to this problem, the more I think that this is absolutely wrong. Can somebody help me with this and maybe explain how to get to the solution?
Thank you!
EDIT
My previous idea was a mix up of definitions, from the comments I now understand that I need to find $I$ (which contains the given matrix), but I'm still confused as to how to do so.
abstract-algebra matrices ring-theory ideals
abstract-algebra matrices ring-theory ideals
asked Jan 4 at 21:20
AlexAlex
304
New contributor
Alex is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Jan 4 at 21:20
AlexAlex
304
New contributor
Alex is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Jan 4 at 22:41
Alex
asked Jan 4 at 21:20
AlexAlex
304
New contributor
Alex is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Jan 4 at 21:20
AlexAlex
304
asked Jan 4 at 21:20
AlexAlex
304
304
New contributor
Alex is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Alex is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Alex is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
3
Ideals are not matrices! Ideals are sets of matrices. You need to find the smallest $I subseteq R$ such that $left(array{1&0&1\1&1&0\0&1&1}right)in I$ and for any $r in R$ and any $i in I$, $ir in I$.
– user3482749
Jan 4 at 21:26
I second what @user3482749 said. It seems that you don't quite understand the definition of ideals, so you need to go back and read it more carefully. What you stated as a "definition" has bits and pieces of the correct one, but the way it's stated doesn't make much sense...
– zipirovich
Jan 4 at 22:25
add a comment |
3
Ideals are not matrices! Ideals are sets of matrices. You need to find the smallest $I subseteq R$ such that $left(array{1&0&1\1&1&0\0&1&1}right)in I$ and for any $r in R$ and any $i in I$, $ir in I$.
– user3482749
Jan 4 at 21:26
I second what @user3482749 said. It seems that you don't quite understand the definition of ideals, so you need to go back and read it more carefully. What you stated as a "definition" has bits and pieces of the correct one, but the way it's stated doesn't make much sense...
– zipirovich
Jan 4 at 22:25
3
3
Ideals are not matrices! Ideals are sets of matrices. You need to find the smallest $I subseteq R$ such that $left(array{1&0&1\1&1&0\0&1&1}right)in I$ and for any $r in R$ and any $i in I$, $ir in I$.
– user3482749
Jan 4 at 21:26
Ideals are not matrices! Ideals are sets of matrices. You need to find the smallest $I subseteq R$ such that $left(array{1&0&1\1&1&0\0&1&1}right)in I$ and for any $r in R$ and any $i in I$, $ir in I$.
– user3482749
Jan 4 at 21:26
I second what @user3482749 said. It seems that you don't quite understand the definition of ideals, so you need to go back and read it more carefully. What you stated as a "definition" has bits and pieces of the correct one, but the way it's stated doesn't make much sense...
– zipirovich
Jan 4 at 22:25
I second what @user3482749 said. It seems that you don't quite understand the definition of ideals, so you need to go back and read it more carefully. What you stated as a "definition" has bits and pieces of the correct one, but the way it's stated doesn't make much sense...
– zipirovich
Jan 4 at 22:25
add a comment |
1 Answer
1
active
oldest
votes
The minimal right ideal of $R$ containing $rin R$ is $rR={rs:sin R}$. In your case it is the set of all products of the form
$$
begin{bmatrix}
1 & 0 & 1 \
1 & 1 & 0 \
0 & 1 & 1 \
end{bmatrix}
begin{bmatrix}
a_{11} & a_{12} & a_{13} \
a_{21} & a_{22} & a_{23} \
a_{31} & a_{32} & a_{33} \
end{bmatrix}
$$
where the second matrix varies through all elements of $R=M_{3}(mathbb{Q})$.
Can this be described more easily, at least in this case? Well, the given matrix is…
answered Jan 4 at 22:50
egregegreg
179k1485202
that's it? just the product of those two matrices? I should've known it wasn't anything too complicated, thank you very much
– Alex
Jan 4 at 23:09
@Alex No, you didn't read carefully or I didn't explain myself too well: it is the set of all matrices of that form, infinitely many of them. But in this particular case, a property of the fixed matrix can be used.
– egreg
Jan 4 at 23:13
no, sorry I have no idea where you're going with this
– Alex
Jan 4 at 23:38
2
@Alex Call $r$ the given matrix. Then $r^{-1}$ exists and belongs to $R$, so among the elements of $rR$ there is $rr^{-1}=1$.
– egreg
Jan 4 at 23:50
okay so the ideal will contain identity??
– Alex
Jan 5 at 0:14
|
show 5 more comments
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Alex is a new contributor. Be nice, and check out our Code of Conduct.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3062124%2fideal-of-matrix-ring%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
The minimal right ideal of $R$ containing $rin R$ is $rR={rs:sin R}$. In your case it is the set of all products of the form
$$
begin{bmatrix}
1 & 0 & 1 \
1 & 1 & 0 \
0 & 1 & 1 \
end{bmatrix}
begin{bmatrix}
a_{11} & a_{12} & a_{13} \
a_{21} & a_{22} & a_{23} \
a_{31} & a_{32} & a_{33} \
end{bmatrix}
$$
where the second matrix varies through all elements of $R=M_{3}(mathbb{Q})$.
Can this be described more easily, at least in this case? Well, the given matrix is…
answered Jan 4 at 22:50
egregegreg
179k1485202
that's it? just the product of those two matrices? I should've known it wasn't anything too complicated, thank you very much
– Alex
Jan 4 at 23:09
@Alex No, you didn't read carefully or I didn't explain myself too well: it is the set of all matrices of that form, infinitely many of them. But in this particular case, a property of the fixed matrix can be used.
– egreg
Jan 4 at 23:13
no, sorry I have no idea where you're going with this
– Alex
Jan 4 at 23:38
2
@Alex Call $r$ the given matrix. Then $r^{-1}$ exists and belongs to $R$, so among the elements of $rR$ there is $rr^{-1}=1$.
– egreg
Jan 4 at 23:50
okay so the ideal will contain identity??
– Alex
Jan 5 at 0:14
|
show 5 more comments
The minimal right ideal of $R$ containing $rin R$ is $rR={rs:sin R}$. In your case it is the set of all products of the form
$$
begin{bmatrix}
1 & 0 & 1 \
1 & 1 & 0 \
0 & 1 & 1 \
end{bmatrix}
begin{bmatrix}
a_{11} & a_{12} & a_{13} \
a_{21} & a_{22} & a_{23} \
a_{31} & a_{32} & a_{33} \
end{bmatrix}
$$
where the second matrix varies through all elements of $R=M_{3}(mathbb{Q})$.
Can this be described more easily, at least in this case? Well, the given matrix is…
answered Jan 4 at 22:50
egregegreg
179k1485202
that's it? just the product of those two matrices? I should've known it wasn't anything too complicated, thank you very much
– Alex
Jan 4 at 23:09
@Alex No, you didn't read carefully or I didn't explain myself too well: it is the set of all matrices of that form, infinitely many of them. But in this particular case, a property of the fixed matrix can be used.
– egreg
Jan 4 at 23:13
no, sorry I have no idea where you're going with this
– Alex
Jan 4 at 23:38
2
@Alex Call $r$ the given matrix. Then $r^{-1}$ exists and belongs to $R$, so among the elements of $rR$ there is $rr^{-1}=1$.
– egreg
Jan 4 at 23:50
okay so the ideal will contain identity??
– Alex
Jan 5 at 0:14
|
show 5 more comments
The minimal right ideal of $R$ containing $rin R$ is $rR={rs:sin R}$. In your case it is the set of all products of the form
$$
begin{bmatrix}
1 & 0 & 1 \
1 & 1 & 0 \
0 & 1 & 1 \
end{bmatrix}
begin{bmatrix}
a_{11} & a_{12} & a_{13} \
a_{21} & a_{22} & a_{23} \
a_{31} & a_{32} & a_{33} \
end{bmatrix}
$$
where the second matrix varies through all elements of $R=M_{3}(mathbb{Q})$.
Can this be described more easily, at least in this case? Well, the given matrix is…
answered Jan 4 at 22:50
egregegreg
179k1485202
The minimal right ideal of $R$ containing $rin R$ is $rR={rs:sin R}$. In your case it is the set of all products of the form
$$
begin{bmatrix}
1 & 0 & 1 \
1 & 1 & 0 \
0 & 1 & 1 \
end{bmatrix}
begin{bmatrix}
a_{11} & a_{12} & a_{13} \
a_{21} & a_{22} & a_{23} \
a_{31} & a_{32} & a_{33} \
end{bmatrix}
$$
where the second matrix varies through all elements of $R=M_{3}(mathbb{Q})$.
Can this be described more easily, at least in this case? Well, the given matrix is…
answered Jan 4 at 22:50
egregegreg
179k1485202
edited Jan 4 at 23:15
answered Jan 4 at 22:50
egregegreg
179k1485202
answered Jan 4 at 22:50
egregegreg
179k1485202
answered Jan 4 at 22:50
egregegreg
179k1485202
179k1485202
that's it? just the product of those two matrices? I should've known it wasn't anything too complicated, thank you very much
– Alex
Jan 4 at 23:09
@Alex No, you didn't read carefully or I didn't explain myself too well: it is the set of all matrices of that form, infinitely many of them. But in this particular case, a property of the fixed matrix can be used.
– egreg
Jan 4 at 23:13
no, sorry I have no idea where you're going with this
– Alex
Jan 4 at 23:38
2
@Alex Call $r$ the given matrix. Then $r^{-1}$ exists and belongs to $R$, so among the elements of $rR$ there is $rr^{-1}=1$.
– egreg
Jan 4 at 23:50
okay so the ideal will contain identity??
– Alex
Jan 5 at 0:14
|
show 5 more comments
that's it? just the product of those two matrices? I should've known it wasn't anything too complicated, thank you very much
– Alex
Jan 4 at 23:09
@Alex No, you didn't read carefully or I didn't explain myself too well: it is the set of all matrices of that form, infinitely many of them. But in this particular case, a property of the fixed matrix can be used.
– egreg
Jan 4 at 23:13
no, sorry I have no idea where you're going with this
– Alex
Jan 4 at 23:38
2
@Alex Call $r$ the given matrix. Then $r^{-1}$ exists and belongs to $R$, so among the elements of $rR$ there is $rr^{-1}=1$.
– egreg
Jan 4 at 23:50
okay so the ideal will contain identity??
– Alex
Jan 5 at 0:14
that's it? just the product of those two matrices? I should've known it wasn't anything too complicated, thank you very much
– Alex
Jan 4 at 23:09
that's it? just the product of those two matrices? I should've known it wasn't anything too complicated, thank you very much
– Alex
Jan 4 at 23:09
@Alex No, you didn't read carefully or I didn't explain myself too well: it is the set of all matrices of that form, infinitely many of them. But in this particular case, a property of the fixed matrix can be used.
– egreg
Jan 4 at 23:13
@Alex No, you didn't read carefully or I didn't explain myself too well: it is the set of all matrices of that form, infinitely many of them. But in this particular case, a property of the fixed matrix can be used.
– egreg
Jan 4 at 23:13
no, sorry I have no idea where you're going with this
– Alex
Jan 4 at 23:38
no, sorry I have no idea where you're going with this
– Alex
Jan 4 at 23:38
2
2
@Alex Call $r$ the given matrix. Then $r^{-1}$ exists and belongs to $R$, so among the elements of $rR$ there is $rr^{-1}=1$.
– egreg
Jan 4 at 23:50
@Alex Call $r$ the given matrix. Then $r^{-1}$ exists and belongs to $R$, so among the elements of $rR$ there is $rr^{-1}=1$.
– egreg
Jan 4 at 23:50
okay so the ideal will contain identity??
– Alex
Jan 5 at 0:14
okay so the ideal will contain identity??
– Alex
Jan 5 at 0:14
|
show 5 more comments
Alex is a new contributor. Be nice, and check out our Code of Conduct.
Alex is a new contributor. Be nice, and check out our Code of Conduct.
Alex is a new contributor. Be nice, and check out our Code of Conduct.
Alex is a new contributor. Be nice, and check out our Code of Conduct.
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3062124%2fideal-of-matrix-ring%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
3
Ideals are not matrices! Ideals are sets of matrices. You need to find the smallest $I subseteq R$ such that $left(array{1&0&1\1&1&0\0&1&1}right)in I$ and for any $r in R$ and any $i in I$, $ir in I$.
– user3482749
Jan 4 at 21:26
I second what @user3482749 said. It seems that you don't quite understand the definition of ideals, so you need to go back and read it more carefully. What you stated as a "definition" has bits and pieces of the correct one, but the way it's stated doesn't make much sense...
– zipirovich
Jan 4 at 22:25