Cokernel of Multiple Matrices Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Does similarity of integer matrices with square $-I$ imply the transition matrix is an integer matrix?Is a specific ring extension $B$ of $K[x,y]$ integrally closed? separable?Intuition for opposite ring, equivalence of left and right modules, anti-involution.Why does flatness imply these Homs are isomorphic?Jacquet modules in representations of finite groupsCohen-Macaulay Analytic RingsA characterization for finitely presented modulesEquivalent definition of maximal Cohen-Macaulay modules over a Gorenstein local ringMatrix factorization hypersurface ringDoes the following property of matrices hold for any commutative ring with identity?
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Cokernel of Multiple Matrices
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Does similarity of integer matrices with square $-I$ imply the transition matrix is an integer matrix?Is a specific ring extension $B$ of $K[x,y]$ integrally closed? separable?Intuition for opposite ring, equivalence of left and right modules, anti-involution.Why does flatness imply these Homs are isomorphic?Jacquet modules in representations of finite groupsCohen-Macaulay Analytic RingsA characterization for finitely presented modulesEquivalent definition of maximal Cohen-Macaulay modules over a Gorenstein local ringMatrix factorization hypersurface ringDoes the following property of matrices hold for any commutative ring with identity?
$begingroup$
Let $R$ be a commutative ring. Given an $mtimes n$ matrix, $A$ over $R$, the cokernel of the matrix is the $R$-module $R^m/textIm(A)$ where $A$ is viewed as an $R$-linear map from $R^n$ to $R^m$. However, I've come across an unfamiliar notation. Given two $mtimes n$ matrices, $A$ and $B$, over $R$, what is meant by $textcok(A,B)$? I encountered this notation in Leuschke and Wiegand's book on Cohen-Macaulay representations.
commutative-algebra notation modules
asked Mar 26 at 7:11
AnonymousAnonymous
36913
$endgroup$
add a comment |
$begingroup$
Let $R$ be a commutative ring. Given an $mtimes n$ matrix, $A$ over $R$, the cokernel of the matrix is the $R$-module $R^m/textIm(A)$ where $A$ is viewed as an $R$-linear map from $R^n$ to $R^m$. However, I've come across an unfamiliar notation. Given two $mtimes n$ matrices, $A$ and $B$, over $R$, what is meant by $textcok(A,B)$? I encountered this notation in Leuschke and Wiegand's book on Cohen-Macaulay representations.
commutative-algebra notation modules
asked Mar 26 at 7:11
AnonymousAnonymous
36913
$endgroup$
add a comment |
$begingroup$
Let $R$ be a commutative ring. Given an $mtimes n$ matrix, $A$ over $R$, the cokernel of the matrix is the $R$-module $R^m/textIm(A)$ where $A$ is viewed as an $R$-linear map from $R^n$ to $R^m$. However, I've come across an unfamiliar notation. Given two $mtimes n$ matrices, $A$ and $B$, over $R$, what is meant by $textcok(A,B)$? I encountered this notation in Leuschke and Wiegand's book on Cohen-Macaulay representations.
commutative-algebra notation modules
asked Mar 26 at 7:11
AnonymousAnonymous
36913
$endgroup$
Let $R$ be a commutative ring. Given an $mtimes n$ matrix, $A$ over $R$, the cokernel of the matrix is the $R$-module $R^m/textIm(A)$ where $A$ is viewed as an $R$-linear map from $R^n$ to $R^m$. However, I've come across an unfamiliar notation. Given two $mtimes n$ matrices, $A$ and $B$, over $R$, what is meant by $textcok(A,B)$? I encountered this notation in Leuschke and Wiegand's book on Cohen-Macaulay representations.
commutative-algebra notation modules
commutative-algebra notation modules
asked Mar 26 at 7:11
AnonymousAnonymous
36913
asked Mar 26 at 7:11
AnonymousAnonymous
36913
asked Mar 26 at 7:11
AnonymousAnonymous
36913
asked Mar 26 at 7:11
AnonymousAnonymous
36913
asked Mar 26 at 7:11
AnonymousAnonymous
36913
36913
add a comment |
add a comment |
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