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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
811
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Proving that $M$ is a simple $R-$module.

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#abstract-algebra #modules #group-actions #module-isomorphism
53
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Understanding how the hint will prove injectivity.

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#abstract-algebra #commutative-algebra #modules #finitely-generated #module-isomorphism
123
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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
144
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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
71
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linearly isomorphic submodule

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#modules #integral-domain #module-isomorphism
68
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A co-isosimple module is co-cyclic.

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#abstract-algebra #ring-theory #modules #module-isomorphism
73
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Does taking covariant Hom commute with taking (co-)kernel?

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#ring-theory #modules #algebras #module-isomorphism
33
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Submodule of a noetherian module is noetherian

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#abstract-algebra #ring-theory #commutative-algebra #modules #module-isomorphism
124
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Prove that the following quotients are isomorphic

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#category-theory #modules #quotient-spaces #module-isomorphism
431
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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
186
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Show that following modules are isomorphic

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#abstract-algebra #modules #module-isomorphism
77
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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
110
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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
35
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Equality of submodules satisfying given conditions - Verification of solution

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#modules #module-isomorphism

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