List questions from module-isomorphism

47

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$f \mapsto b, b(r,m)=r\cdot f(m)$ gives an isomorphism of $R$-modules $\Phi_N : \text {Hom}_R(M,N) \rightarrow \text {Bilin}_R(R×M,N)$

Published on 09 Oct 2023 - 22:17

14

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Show that the statements about module $M_R$ are equivalent.

Published on 12 Oct 2023 - 18:41

33

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cyclic $R$-module correspondence in $R$ which is PID

Published on 13 Oct 2023 - 9:42

103

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The inverse map of the Poincare duality map

Published on 23 Feb 2026 - 4:59

81

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Serre conditions and local isomorphisms

Published on 25 Mar 2026 - 14:29

60

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On the homomorphism as $M_n(A)$-modules.

Published on 04 Nov 2023 - 20:27

74

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How Should I Prove that the Localization of Quotients Commute from here?

Published on 08 Nov 2023 - 19:16

53

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Module over $R$ isomorphic to $R$ itself

Published on 17 Nov 2023 - 13:23

82

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$\mathrm{Hom}_R (R/(x),R)\cong M$ for $R=k[x,y]/(xy)$. $M=R/(x)$

Published on 29 Nov 2023 - 20:58

123

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Theorem 7, Section 4.5 of Hungerford’s Algebra

Published on 14 Feb 2024 - 18:57

45

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Sheaf of isomorphisms of $\mathcal{O}_X$-modules

Published on 27 Feb 2024 - 23:14

31

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Why in the following problem the author take the left ideal in the following form?

Published on 30 Oct 2017 - 8:00

1.1k

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Prove that if A is simple every R-module endomorphism is either the zero map or an isomorphism.

Published on 30 Oct 2017 - 18:07

61

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Submodules and isomorphisms

Published on 01 Nov 2017 - 18:34

42

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Finding an isomorhpism $A_n \cong \mathbb{Z}/(m,n)\mathbb{Z}$

Published on 06 Nov 2017 - 4:36

List Question

$f \mapsto b, b(r,m)=r\cdot f(m)$ gives an isomorphism of $R$-modules $\Phi_N : \text {Hom}_R(M,N) \rightarrow \text {Bilin}_R(R×M,N)$

Show that the statements about module $M_R$ are equivalent.

cyclic $R$-module correspondence in $R$ which is PID

The inverse map of the Poincare duality map

Serre conditions and local isomorphisms

On the homomorphism as $M_n(A)$-modules.

How Should I Prove that the Localization of Quotients Commute from here?

Module over $R$ isomorphic to $R$ itself

$\mathrm{Hom}_R (R/(x),R)\cong M$ for $R=k[x,y]/(xy)$. $M=R/(x)$

Theorem 7, Section 4.5 of Hungerford’s Algebra

Sheaf of isomorphisms of $\mathcal{O}_X$-modules

Why in the following problem the author take the left ideal in the following form?

Prove that if A is simple every R-module endomorphism is either the zero map or an isomorphism.

Submodules and isomorphisms

Finding an isomorhpism $A_n \cong \mathbb{Z}/(m,n)\mathbb{Z}$

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