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15
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Prove that any free module with finite basis is projective

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#abstract-algebra #ring-theory #modules #projective-module
91
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Endomorphism ring of an irreducible module is irreducible

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#abstract-algebra #modules #direct-sum
552
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Question about abelian groups, $\mathbb{Z}$-modules and homomorphisms.

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#abstract-algebra #modules #abelian-groups #group-homomorphism
59
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Examples of modules over commutative rings with rich structure

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#modules #examples-counterexamples
218
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Show that if $R/A$ is IBN then $R$ is IBN.

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#abstract-algebra #proof-verification #ring-theory #modules #free-modules
148
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Subspaces and submodules of $k[x,y]$

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#polynomials #vector-spaces #modules #involutions
179
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If $M_m=0\forall m\in \operatorname{Specm}(A)$ s.t. $m\supset I$, then $M=IM$

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#commutative-algebra #modules #maximal-and-prime-ideals #localization
79
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Show that $1\otimes i $ is injective.

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#abstract-algebra #commutative-algebra #modules #tensor-products #flatness
62
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If $E\cong F$ and $E\subset F$, can we say that $E=F$?

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#abstract-algebra #commutative-algebra #modules
119
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Definition of a module in Humphreys

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#abstract-algebra #modules #representation-theory #lie-algebras
87
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Can we say that the following diagram is commutative?

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#abstract-algebra #ring-theory #commutative-algebra #category-theory #modules
338
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What is the structure of a finite rank torsion-free module over a DVR?

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#commutative-algebra #modules
77
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Universal Property of Products in $A$-modules

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#commutative-algebra #modules #direct-sum #direct-product
65
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Is the homomorphism induced on symmetric algebras injective?

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#abstract-algebra #ring-theory #commutative-algebra #modules
103
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Natural Isomorphism of Tensor Product With Two Rings

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#linear-algebra #modules #tensor-products

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