List questions from commutative-algebra | MathQA

If $f(t)\in 1 + t\mathbb{Z}[t]$ is irred., could there exist arbitrarily large $n$ such that for some $a\in\mathbb{Z}$, $f(t)+at^n$ splits completely?

Published on 14 Feb 2018 - 22:06

$A^n\cong A^m$ implies $n=m$ without using tensor products.

Published on 15 Feb 2018 - 14:44

Show $S[[x]]\rightarrow K^{(x)}$ is surjective

Published on 25 Mar 2026 - 18:54

Valuation ring lying between a valuation ring and its fraction field

Published on 25 Mar 2026 - 11:53

composition of finite morphism

Published on 16 Feb 2018 - 15:21

Geometric interpretation of the Noether normalization lemma

Published on 16 Feb 2018 - 15:22

Example of a noetherian domain which is neither Dedekind domain nor UFD?

Published on 16 Feb 2018 - 18:35

Completion w.r.t. regular maximal ideal

Published on 16 Feb 2018 - 20:08

localization of a free f.g. k-algebra at a prime ideal

Published on 25 Mar 2026 - 14:16

Checking if quotient ring is Noetherian or Artinian over a module

Published on 22 Mar 2026 - 17:24

Localization of PID, if DVR, is a localization at a prime ideal

Published on 20 Mar 2026 - 6:05

Associated primes to principal ideals in a Noetherian domain

Published on 19 Mar 2026 - 23:41

Proof explanation, singular point of an affine variety

Published on 17 Feb 2018 - 18:46

What does it mean for an element to generate a field as an F-algebra?

Published on 25 Mar 2026 - 3:07

A Presheaf satisfying a sort of Unique Gluing axiom is a Sheaf ?

Published on 25 Mar 2026 - 1:18