List questions from principal-ideal-domains

Published on 19 Jul 2017 - 16:03

213

Views

Triangularization of matrix over PID

Published on 27 Mar 2026 - 13:16

244

Views

Finitely generated module over a quotient of a PID

Published on 18 Aug 2017 - 23:23

200

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Is this a valid proof that a finitely generated torsion-free module over a PID is free?

Published on 30 Aug 2017 - 22:24

1.9k

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$A=\frac{\mathbb{C}[X,Y]}{(X^2+Y^2-1)}$ is a PID.

Published on 30 Mar 2026 - 2:06

142

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$a,b$ co-prime elements in PID $R$ , then to show $R[X]/(aX-b) \cong R[1/a]$

Published on 30 Mar 2026 - 17:35

172

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Is $R[r]$ equal to $R$ itself? And some consequences

Published on 05 Sep 2017 - 12:29

444

Views

Finding the finitely generated indecomposable modules over a given ring

Published on 29 Mar 2026 - 12:03

168

Views

Question about $R$ modules are precisely $k[x]$ modules which are annihilated by $\langle x^p \rangle$?

Published on 29 Mar 2026 - 12:12

375

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Is there a way to determine the kernel of the map $f: M \to F \otimes M$ defined by $x \mapsto 1 \otimes x$?

Published on 08 Sep 2017 - 4:58

1.3k

Views

Generator of an ideal in the polynomial ring $ F[x] $ for a field $ F $

Published on 10 Sep 2017 - 3:51

42

Views

Isomorphism of finite generated modules

Published on 10 Sep 2017 - 18:51

929

Views

A Simpler proof for a Principal Ideal Domain which is not a Euclidean Domain

Published on 27 Mar 2026 - 0:43

1.2k

Views

When is $\mathbb Z[\zeta_n]$ a Euclidean Domain?

Published on 27 Mar 2026 - 0:36

567

Views

Description of the lattice that gcd and lcm form on a PID

Published on 24 Feb 2026 - 10:17

List Question

$p$ is prime if and only if $p$ is irreducible

Triangularization of matrix over PID

Finitely generated module over a quotient of a PID

Is this a valid proof that a finitely generated torsion-free module over a PID is free?

$A=\frac{\mathbb{C}[X,Y]}{(X^2+Y^2-1)}$ is a PID.

$a,b$ co-prime elements in PID $R$ , then to show $R[X]/(aX-b) \cong R[1/a]$

Is $R[r]$ equal to $R$ itself? And some consequences

Finding the finitely generated indecomposable modules over a given ring

Question about $R$ modules are precisely $k[x]$ modules which are annihilated by $\langle x^p \rangle$?

Is there a way to determine the kernel of the map $f: M \to F \otimes M$ defined by $x \mapsto 1 \otimes x$?

Generator of an ideal in the polynomial ring $ F[x] $ for a field $ F $

Isomorphism of finite generated modules

A Simpler proof for a Principal Ideal Domain which is not a Euclidean Domain

When is $\mathbb Z[\zeta_n]$ a Euclidean Domain?

Description of the lattice that gcd and lcm form on a PID

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