List questions from modules

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For a semi-simple ring $R$ and $R$-module $M$ show TFAE: M finitely generated, artinian and noetherian.

Published on 14 Apr 2026 - 19:34

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Equivalent conditions for a finitely presented module

Published on 15 Apr 2026 - 7:13

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Direct sum of modules if and only if is sum without intersection.

Published on 12 Apr 2026 - 6:37

384

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Equivalent conditions for a finite module over a Noetherian domain

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538

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Finitely generated module and free module.

Published on 15 Apr 2026 - 4:37

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$A\cong \Bbb Z_{(p)}\otimes A$ if multiplication by $n$ is iso

Published on 13 Apr 2026 - 19:52

80

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Zero elements of tensor product of two free modules

Published on 14 Apr 2026 - 20:05

650

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$\Bbb Z_{(p)}\otimes_{\Bbb Z} \Bbb Z/q^k$ is zero?

Published on 14 Apr 2026 - 16:57

25

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$R=F[x]$, $A=[v_1,\ldots,v_n]\in \operatorname{Mat}_n(R)$, $M=R^n/(Rv_1+\cdots+Rv_n)$ Then $M$ is finite dimensional over $F$ iff $f=\det(A)\ne 0$

Published on 16 Apr 2026 - 13:30

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A property of faithfully flat modules

Published on 15 Apr 2026 - 10:44

433

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Equivalent conditions for a faithfully flat module

Published on 15 Apr 2026 - 18:34

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Does every finitary monad with this propery arise as a free module monad?

Published on 25 Mar 2026 - 12:54

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Finding all simple modules over path algebra of given quiver

Published on 10 Apr 2026 - 18:22

114

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Counterexample to $F\otimes_R k(P)\ne 0$ iff $IF\ne F$ for $F$ flat

Published on 16 Apr 2026 - 19:52

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Cohomology of finite cyclic group is always torsion

For a semi-simple ring $R$ and $R$-module $M$ show TFAE: M finitely generated, artinian and noetherian.

Equivalent conditions for a finitely presented module

Direct sum of modules if and only if is sum without intersection.

Equivalent conditions for a finite module over a Noetherian domain

Finitely generated module and free module.

$A\cong \Bbb Z_{(p)}\otimes A$ if multiplication by $n$ is iso

Zero elements of tensor product of two free modules

$\Bbb Z_{(p)}\otimes_{\Bbb Z} \Bbb Z/q^k$ is zero?

$R=F[x]$, $A=[v_1,\ldots,v_n]\in \operatorname{Mat}_n(R)$, $M=R^n/(Rv_1+\cdots+Rv_n)$ Then $M$ is finite dimensional over $F$ iff $f=\det(A)\ne 0$

A property of faithfully flat modules

Equivalent conditions for a faithfully flat module

Does every finitary monad with this propery arise as a free module monad?

Finding all simple modules over path algebra of given quiver

Counterexample to $F\otimes_R k(P)\ne 0$ iff $IF\ne F$ for $F$ flat

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