List questions from commutative-algebra

Published on 14 Apr 2026 - 18:35

771

Views

Are Dummit and Foote making a mistake in proving Cohen's theorem?

Published on 11 Apr 2026 - 22:29

89

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Maximal among some ideals is prime

Published on 12 Apr 2026 - 11:14

172

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Inversion of an element in Picard group over commutative ring

Published on 29 Apr 2026 - 12:41

104

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Given an ideal of a ring $R$, is there any way by which the associated primes of $R/I$ can be computed without knowing a primary decomposition of $I$?

Published on 14 Apr 2026 - 18:18

177

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On Bounded Index of Nilpotency of $R[x]$ and $M_n(R)$

Published on 16 Apr 2026 - 13:53

277

Views

Counterexamples in $R$-modules products and $R$-modules direct sums and $R$-homomorphisms (Exemplification)

Published on 16 Apr 2026 - 11:19

277

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If $\mathfrak a\subset A$ is a finitely generated ideal, and if $\mathfrak p$ is a prime ideal, then $S(\mathfrak a)\cap\mathfrak p\not=\emptyset ?$

Published on 14 Apr 2026 - 22:32

1k

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Intersection of two flat submodules

Published on 13 Apr 2026 - 23:15

456

Views

How to check if an ideal is primary

Published on 09 Apr 2026 - 3:27

239

Views

Prime ideal $P$ in $R$ coprime to the conductor plus the localization $R_{P}$ is a DVR implies that $P$ is invertible

Published on 15 Apr 2026 - 4:23

1.3k

Views

Other proof for tensor product equal to zero (without use Nakayama lemma and Jacobson radical)

Published on 12 Apr 2026 - 23:23

52

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Simultaneous congruences

Published on 13 Apr 2026 - 3:49

132

Views

Basic algebraic geometry question (confused about conventions)

Published on 11 Apr 2026 - 20:33

177

Views

A certain natural map between Tor functors

Published on 14 Apr 2026 - 0:09

List Question

$S^{-1}R[(x_i)_{i\in I}]=(S^{-1}R)[(x_i)_{i\in I}]$

Are Dummit and Foote making a mistake in proving Cohen's theorem?

Maximal among some ideals is prime

Inversion of an element in Picard group over commutative ring

Given an ideal of a ring $R$, is there any way by which the associated primes of $R/I$ can be computed without knowing a primary decomposition of $I$?

On Bounded Index of Nilpotency of $R[x]$ and $M_n(R)$

Counterexamples in $R$-modules products and $R$-modules direct sums and $R$-homomorphisms (Exemplification)

If $\mathfrak a\subset A$ is a finitely generated ideal, and if $\mathfrak p$ is a prime ideal, then $S(\mathfrak a)\cap\mathfrak p\not=\emptyset ?$

Intersection of two flat submodules

How to check if an ideal is primary

Prime ideal $P$ in $R$ coprime to the conductor plus the localization $R_{P}$ is a DVR implies that $P$ is invertible

Other proof for tensor product equal to zero (without use Nakayama lemma and Jacobson radical)

Simultaneous congruences

Basic algebraic geometry question (confused about conventions)

A certain natural map between Tor functors

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