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Isomorphism in Projective modules over the algebraic closure of a finite field Fp

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#commutative-algebra #finite-fields #tensor-products #projective-module #module-isomorphism
266
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Is the direct sum preserved under isomorphism

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#modules #exact-sequence #free-modules #group-rings #module-isomorphism
78
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Does an isomorphism between extension of scalars implies an isomorphism of original modules

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#modules #homological-algebra #adjoint-functors #local-rings #module-isomorphism
67
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Module examples

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#modules #module-isomorphism
121
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Isomorphism of associated graded of modules with increasing exhaustive filtrations induces an isomorphism of the modules

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#abstract-algebra #graded-modules #module-isomorphism #filtered-modules
133
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$R$-module isomorphisms $M/A\cong B$ And $M/B\cong A$

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#abstract-algebra #modules #quotient-group #module-isomorphism
135
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A module has only finite many submodule up to isomorphism

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#commutative-algebra #modules #artinian #module-isomorphism
115
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Surjective Endomorphisms of finitley generated modules are isomorphisms

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#abstract-algebra #commutative-algebra #modules #module-isomorphism
77
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Isomorphism under restriction

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#representation-theory #dual-spaces #module-isomorphism
48
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$\mathbb{R}(n)$ is a simple algebra

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#abstract-algebra #matrices #ideals #semi-simple-rings #module-isomorphism
67
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Cross-multiplication theorem of quotient modules.

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#abstract-algebra #modules #quotient-spaces #direct-sum #module-isomorphism
43
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$T^{-1}(N \otimes_A M) \cong T^{-1}N \otimes_A M$

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#ring-theory #commutative-algebra #modules #tensor-products #module-isomorphism
78
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Implications of $R \cong M_n (D)$ for division ring $D$

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#modules #module-isomorphism
35
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Artin-Wedderburn baby version

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#modules #group-homomorphism #module-isomorphism
96
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Let $M$ be an $A$-module. Prove that $\operatorname{Hom}_A(A,M) \cong M$.

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#abstract-algebra #solution-verification #commutative-algebra #modules #module-isomorphism

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