List questions from principal-ideal-domains

46

Views

Defining an evaluation map between $\mathbb{Q}\lbrack x \rbrack$ and $\mathbb{Q}\lbrack x \rbrack/(x^2-5)$

Published on 25 Mar 2026 - 10:55

29

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Given $k$, for every $n>1$, constructing a set of size $n$ of non-zero integers having gcd $k$ so that no proper subset has gcd $k$

Published on 26 Mar 2026 - 13:52

107

Views

Axes of a free module over a PID

Published on 25 Mar 2026 - 6:50

243

Views

$\mathbb{Z}$-Module exercise

Published on 26 Mar 2026 - 23:26

59

Views

Axes of a free module over a PID (2)

Published on 25 Mar 2026 - 6:50

193

Views

Prove polynomial ring over a discrete valuation ring quotient by powers of maximal ideal is regular?

Published on 20 Mar 2026 - 10:04

516

Views

Set of all R-homomorphism is finitely generated

Published on 25 Mar 2026 - 17:40

45

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Is still true that every nonzero Prime Ideal is Maximal in a noncommutative PID?

Published on 22 Feb 2019 - 15:05

66

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Is this necessary for the first structure theorem for modules?

Published on 02 Mar 2019 - 11:33

128

Views

Showing that ideals are principal in ring of integers of cubic field

Published on 02 Mar 2019 - 19:09

237

Views

Showing if $R$ is a PID and $0\neq r\in R$ is irreducible, then $R[X]/(r)\cong (R/(r))[X]$

Published on 25 Mar 2026 - 10:58

53

Views

Irreducible Subring in Q

Published on 04 Mar 2019 - 9:31

174

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$Rx/Rax \simeq R/Ra$ whenever $\mathrm{Ann}(x)=\{0\}$

Published on 05 Mar 2019 - 21:11

275

Views

Prove that the quotient ring is not a PID

Published on 25 Mar 2026 - 7:41

35

Views

Help understanding a lemma on modules over a PID.

Published on 06 Mar 2019 - 0:59

List Question

Defining an evaluation map between $\mathbb{Q}\lbrack x \rbrack$ and $\mathbb{Q}\lbrack x \rbrack/(x^2-5)$

Given $k$, for every $n>1$, constructing a set of size $n$ of non-zero integers having gcd $k$ so that no proper subset has gcd $k$

Axes of a free module over a PID

$\mathbb{Z}$-Module exercise

Axes of a free module over a PID (2)

Prove polynomial ring over a discrete valuation ring quotient by powers of maximal ideal is regular?

Set of all R-homomorphism is finitely generated

Is still true that every nonzero Prime Ideal is Maximal in a noncommutative PID?

Is this necessary for the first structure theorem for modules?

Showing that ideals are principal in ring of integers of cubic field

Showing if $R$ is a PID and $0\neq r\in R$ is irreducible, then $R[X]/(r)\cong (R/(r))[X]$

Irreducible Subring in Q

$Rx/Rax \simeq R/Ra$ whenever $\mathrm{Ann}(x)=\{0\}$

Prove that the quotient ring is not a PID

Help understanding a lemma on modules over a PID.

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