List questions from modules

Published on 09 Apr 2026 - 17:03

1.4k

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Properties characterized by a vanishing Ext or Tor module

Published on 15 Apr 2026 - 9:21

855

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Universal property of tensor product of $R$-algebras

Published on 15 Apr 2026 - 18:08

27

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Why do we take $R$ when constructing the tensor algebra?l

Published on 11 Apr 2026 - 0:11

677

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Can every $T$-stable subspace be realised as the kernel of another linear operator that commutes with$~T$?

Published on 11 Apr 2026 - 0:34

44

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What's actually $S^k(M)$?

Published on 28 Apr 2026 - 12:16

37

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What condition is necessary to form a quotient algebra?

Published on 12 Apr 2026 - 19:30

117

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Is it okay to define k-th symmetric power of $M$ in this way?

Published on 28 Apr 2026 - 13:52

65

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Integral group ring quotient as a right module

Published on 12 Apr 2026 - 14:17

268

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equivalent condition for finitely generated module

Published on 16 Apr 2026 - 9:38

830

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Is the symmetric algebra direct sum of $k$-th symmetric powers?

Published on 27 Mar 2026 - 23:37

1.2k

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$M' \to M \to M'' \to 0$ exact $\implies 0\to \text{Hom}(M'',N) \to \text{Hom}(M,N) \to \text{Hom}(M',N)$ is exact.

Published on 17 Apr 2026 - 2:32

77

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Proving that $\det(A)R^n \subset\mathrm{Im}(\Phi)$

Published on 18 Apr 2026 - 5:51

2.1k

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Is the kernel of a map to a finitely presented module finitely generated?

Published on 11 Apr 2026 - 12:04

150

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Can matrix representation be extended to free modules?

Published on 13 Apr 2026 - 19:16

List Question

Easy proof from Atiyah-McDonald on module homomorphisms

Properties characterized by a vanishing Ext or Tor module

Universal property of tensor product of $R$-algebras

Why do we take $R$ when constructing the tensor algebra?l

Can every $T$-stable subspace be realised as the kernel of another linear operator that commutes with$~T$?

What's actually $S^k(M)$?

What condition is necessary to form a quotient algebra?

Is it okay to define k-th symmetric power of $M$ in this way?

Integral group ring quotient as a right module

equivalent condition for finitely generated module

Is the symmetric algebra direct sum of $k$-th symmetric powers?

$M' \to M \to M'' \to 0$ exact $\implies 0\to \text{Hom}(M'',N) \to \text{Hom}(M,N) \to \text{Hom}(M',N)$ is exact.

Proving that $\det(A)R^n \subset\mathrm{Im}(\Phi)$

Is the kernel of a map to a finitely presented module finitely generated?

Can matrix representation be extended to free modules?

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