List questions from principal-ideal-domains

Published on 25 Mar 2026 - 9:23

250

Views

Let $D$ be a UFD such that Bezout's Identity holds. Then Every ideal is finitely generated implies that $D$ is PID

Published on 23 Nov 2019 - 16:31

35

Views

If $M=D/(d)$ then $M=t_{p}(M)\oplus t_{q}(M)$

Published on 26 Mar 2026 - 9:46

86

Views

Prime and maximal ideals of $\mathbb{C}[x,y]$.

Published on 07 Dec 2019 - 13:32

116

Views

If $A$ is a DVR such that $k\subset A\subset k(x)$, $Frac(A)=k(x)$ and $x\not\in A$, then $A=\mathcal{O}_{\infty}(k)$

Published on 26 Mar 2026 - 3:01

374

Views

Constructing invertible matrix with entries in a principal ideal domain

Published on 12 Dec 2019 - 19:57

555

Views

Suppose $a$ is odd and $b$ is even. Prove that $\operatorname{gcd}(a,b) = \operatorname{gcd}(a+b, a-b)$.

Published on 14 Dec 2019 - 22:17

193

Views

$R$ is not a principal ideal domain (show)

Published on 30 Dec 2019 - 12:06

165

Views

Proof: PID is UFD: not understanding step

Published on 04 Jan 2020 - 14:40

268

Views

Number of ideals of norm $100$ of the Kleinian integers

Published on 26 Mar 2026 - 12:37

54

Views

Homomorphisms between $R/(p_1^{e_1})$ and $R/(p_2^{e_2})$ when $p_1$ and $p_2$ are associated.

Published on 25 Mar 2026 - 17:39

89

Views

Module in exact sequence isomorphism

Published on 27 Mar 2026 - 0:01

622

Views

Let R be a principal ideal ring, prove R is a Noetherian ring.

Published on 26 Mar 2026 - 8:04

130

Views

Prove that an ideal of a subring of $\mathbb{Q}$ is principal

Published on 26 Mar 2026 - 14:21

401

Views

Uniqueness of generator of Principal ideal domain

Published on 29 Jan 2020 - 15:10

List Question

Counterexample: Local Artinian ring is not a PID

Let $D$ be a UFD such that Bezout's Identity holds. Then Every ideal is finitely generated implies that $D$ is PID

If $M=D/(d)$ then $M=t_{p}(M)\oplus t_{q}(M)$

Prime and maximal ideals of $\mathbb{C}[x,y]$.

If $A$ is a DVR such that $k\subset A\subset k(x)$, $Frac(A)=k(x)$ and $x\not\in A$, then $A=\mathcal{O}_{\infty}(k)$

Constructing invertible matrix with entries in a principal ideal domain

Suppose $a$ is odd and $b$ is even. Prove that $\operatorname{gcd}(a,b) = \operatorname{gcd}(a+b, a-b)$.

$R$ is not a principal ideal domain (show)

Proof: PID is UFD: not understanding step

Number of ideals of norm $100$ of the Kleinian integers

Homomorphisms between $R/(p_1^{e_1})$ and $R/(p_2^{e_2})$ when $p_1$ and $p_2$ are associated.

Module in exact sequence isomorphism

Let R be a principal ideal ring, prove R is a Noetherian ring.

Prove that an ideal of a subring of $\mathbb{Q}$ is principal

Uniqueness of generator of Principal ideal domain

Trending Questions

Popular # Hahtags

Popular Questions