List questions from modules

Published on 15 Apr 2026 - 22:55

616

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An exercise on tensor product over an integral domain.

Published on 11 Apr 2026 - 6:27

380

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Existence of projection in proof of Maschke's theorem

Published on 13 Apr 2026 - 23:09

44

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Presented matrix and number ring.

Published on 14 Apr 2026 - 22:36

68

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Prove that $I_k \otimes_k \Omega \rightarrow I$ is injective

Published on 15 Apr 2026 - 13:47

574

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An exercise using Nakayama's lemma.

Published on 12 Apr 2026 - 5:24

47

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Question on the argument proving primary decomposition theorem

Published on 18 Apr 2026 - 6:52

1.6k

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In a split short exact sequence of modules, is the third term always free?

Published on 14 Apr 2026 - 3:45

2.6k

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Is the image of a ring homomorphism an ideal?

Published on 13 Apr 2026 - 4:25

68

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Why is $\text{End}_K(K) = K$, or, more generally, $\text{End}_D(D) = D^{\text{op}}$?

Published on 17 Apr 2026 - 14:06

485

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Depth comparison on short exact sequences

Published on 12 Apr 2026 - 12:14

381

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every projective module has a free complement.

Published on 14 Apr 2026 - 12:59

90

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Castelnuovo-Mumford regularity of a shifted module

Published on 16 Apr 2026 - 13:16

245

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Character of action of permutations on a subset

Published on 13 Apr 2026 - 8:19

2.3k

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A ring without the Invariant Basis Number property

Published on 12 Apr 2026 - 20:50

List Question

Let $R$ be a domain. Then $\operatorname{Tor}_n^R(A,B)$ is a torsion module

An exercise on tensor product over an integral domain.

Existence of projection in proof of Maschke's theorem

Presented matrix and number ring.

Prove that $I_k \otimes_k \Omega \rightarrow I$ is injective

An exercise using Nakayama's lemma.

Question on the argument proving primary decomposition theorem

In a split short exact sequence of modules, is the third term always free?

Is the image of a ring homomorphism an ideal?

Why is $\text{End}_K(K) = K$, or, more generally, $\text{End}_D(D) = D^{\text{op}}$?

Depth comparison on short exact sequences

every projective module has a free complement.

Castelnuovo-Mumford regularity of a shifted module

Character of action of permutations on a subset

A ring without the Invariant Basis Number property

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