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Extension of scalars functor essentially surjective.

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#abstract-algebra #commutative-algebra #modules #tensor-products
350
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Radical series and simple factors in the composition series

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#abstract-algebra #modules
58
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Basis of a finite free $R$-algebra starting with $1$ , $R$ is local

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#abstract-algebra #modules #noncommutative-algebra
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Why $\mathbb Z/2\mathbb Z$ is not free as $\mathbb Z$-module?

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#abstract-algebra #modules
191
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The tensor product of algebras is associative if both of the algebras are associative.

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#abstract-algebra #modules #tensor-products #associativity
776
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Property of short exact sequences.

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#abstract-algebra #modules #exact-sequence
146
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$\mathrm{Hom}(\lim_IA_i,B)=\mathrm{colim}_I(\mathrm{Hom}(A_i,B))$?

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#abstract-algebra #category-theory #modules #homological-algebra
93
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Does there exist such a module?

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#abstract-algebra #modules
374
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Can a nonzero module be cocompact?

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#abstract-algebra #category-theory #modules #homological-algebra #limits-colimits
281
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Proof of a corollary to Nakayama's lemma

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#linear-algebra #vector-spaces #commutative-algebra #modules
204
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Why do we not need to show that $a-b \in W$ to verify that $W$ is a subspace?

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#abstract-algebra #group-theory #vector-spaces #modules
393
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The localization of a module at a prime is zero

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#commutative-algebra #modules #localization
245
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Isomorphism R-module and quotient modules

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#abstract-algebra #modules
90
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The definition of minimal faithful module in QF-3 algebra

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#modules #representation-theory
53
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Existence of an element in a ring with a given property

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#abstract-algebra #commutative-algebra #modules #ideals #maximal-and-prime-ideals

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