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Scalar extension preserves isomorphisms

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#abstract-algebra #category-theory #functors #module-isomorphism
38
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Isomorphism Preserves Containment on Modules?

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#abstract-algebra #module-isomorphism
31
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Presentations of Modules by Similar Matrices

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#abstract-algebra #ring-theory #free-modules #module-isomorphism
101
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The direct sum of modules is generated by their union

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#modules #direct-sum #direct-product #free-modules #module-isomorphism
107
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Do module isomorphisms preserve freeness?

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#category-theory #free-modules #module-isomorphism
44
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In a commutative ring with unity, two unital cyclic R-modules are isomorphic iff they have the annihilators

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#abstract-algebra #modules #module-isomorphism
93
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Why does extending scalars from $R$ to $S$ preserve isomorphism?

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#vector-spaces #commutative-algebra #field-theory #module-isomorphism
39
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Let $x,y,z,t$ be elements of a ring $R$ such that $xz=yt=1,xt=yz=0$ and $zx+ty=1$. Prove that the left $R$-modules $R$ and $R \oplus R$ are isomorphic

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#ring-theory #modules #module-isomorphism
52
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Prove that a module over a subring of matrices is isomorphic to a direct sum of vector spaces over that ring

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#abstract-algebra #modules #module-isomorphism
65
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Is the the shift functor exact

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#abstract-algebra #homology-cohomology #homological-algebra #module-isomorphism
84
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Annihilator of a module homomorphism

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#abstract-algebra #homological-algebra #quotient-spaces #module-isomorphism
73
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Commutative diagram between modules and their double dual

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#abstract-algebra #modules #diagram-chasing #module-isomorphism
98
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Proof of First Isomorphism Theorem for $R$-Modules

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#category-theory #module-isomorphism
242
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When two infinite direct products $\prod_I\Bbb{Z}$ and $ \prod_J\Bbb{Z}$ are isomorphic?

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#group-theory #ring-theory #abelian-groups #module-isomorphism
34
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Construct isomorphism $M\cong M/N+N$?

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#abstract-algebra #modules #module-isomorphism

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