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Do I have to show that elements of $L$ commutes with elements of $N$ (like in case of direct product) and if so, why?

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#abstract-algebra #solution-verification #modules #exact-sequence #module-isomorphism
812
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Proving that $M$ is a simple $R-$module.

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#abstract-algebra #modules #group-actions #module-isomorphism
54
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Understanding how the hint will prove injectivity.

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#abstract-algebra #commutative-algebra #modules #finitely-generated #module-isomorphism
124
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Proving $r(m + n) = rm + rn$ for a type of scalar multiplication.

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#abstract-algebra #proof-explanation #modules #tensor-products #module-isomorphism
145
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Understanding example 3 on pg. 369 in Dummit & Foote (3rd edition)

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#abstract-algebra #ring-theory #modules #tensor-products #module-isomorphism
72
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linearly isomorphic submodule

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#modules #integral-domain #module-isomorphism
69
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A co-isosimple module is co-cyclic.

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#abstract-algebra #ring-theory #modules #module-isomorphism
74
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Does taking covariant Hom commute with taking (co-)kernel?

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#ring-theory #modules #algebras #module-isomorphism
34
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Submodule of a noetherian module is noetherian

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#abstract-algebra #ring-theory #commutative-algebra #modules #module-isomorphism
125
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Prove that the following quotients are isomorphic

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#category-theory #modules #quotient-spaces #module-isomorphism
434
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Hom( , ) and Hom_F( , ) and tensor product

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#abstract-algebra #tensor-products #group-homomorphism #free-groups #module-isomorphism
187
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Show that following modules are isomorphic

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#abstract-algebra #modules #module-isomorphism
78
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A semiprime right semihereditary ring R is right isonoetherian or right uniform if and only if it is right nei-Noetherian.

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#abstract-algebra #ring-theory #modules #module-isomorphism
111
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Proof verification of showing that $M\otimes A/{\frak a} \cong M/{\frak a}M$

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#abstract-algebra #solution-verification #tensor-products #module-isomorphism
36
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Equality of submodules satisfying given conditions - Verification of solution

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#modules #module-isomorphism

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