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

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#abstract-algebra #ring-theory #modules #bilinear-form #module-isomorphism
15
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Show that the statements about module $M_R$ are equivalent.

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#modules #projective-module #module-isomorphism
34
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cyclic $R$-module correspondence in $R$ which is PID

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#abstract-algebra #modules #ideals #module-isomorphism
105
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The inverse map of the Poincare duality map

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#algebraic-topology #duality-theorems #module-isomorphism #poincare-duality
81
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Serre conditions and local isomorphisms

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#commutative-algebra #homological-algebra #local-rings #cohen-macaulay #module-isomorphism
61
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On the homomorphism as $M_n(A)$-modules.

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#modules #ring-homomorphism #algebras #module-isomorphism
75
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How Should I Prove that the Localization of Quotients Commute from here?

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#abstract-algebra #modules #exact-sequence #localization #module-isomorphism
54
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Module over $R$ isomorphic to $R$ itself

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#abstract-algebra #ring-theory #modules #module-isomorphism
83
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$\mathrm{Hom}_R (R/(x),R)\cong M$ for $R=k[x,y]/(xy)$. $M=R/(x)$

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#abstract-algebra #homological-algebra #module-isomorphism
124
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Theorem 7, Section 4.5 of Hungerford’s Algebra

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#abstract-algebra #proof-writing #modules #tensor-products #module-isomorphism
46
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Sheaf of isomorphisms of $\mathcal{O}_X$-modules

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#abstract-algebra #sheaf-theory #module-isomorphism
32
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Why in the following problem the author take the left ideal in the following form?

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#abstract-algebra #modules #module-isomorphism
1.1k
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Prove that if A is simple every R-module endomorphism is either the zero map or an isomorphism.

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#abstract-algebra #modules #module-isomorphism
63
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Submodules and isomorphisms

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#ring-theory #modules #module-isomorphism
43
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Finding an isomorhpism $A_n \cong \mathbb{Z}/(m,n)\mathbb{Z}$

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#modules #module-isomorphism

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