Question

lcm$(p(x),q(x)) \cdot \gcd(p(x),q(x)) \sim p(x)q(x)$ holds for $D[x]$ with D u.f.d?

score 30 · Answer 1 · 2026-04-17 02:28:14

30

Views

lcm$(p(x),q(x)) \cdot \gcd(p(x),q(x)) \sim p(x)q(x)$ holds for $D[x]$ with D u.f.d?

Published on 17 Apr 2026 - 2:28

score 290 · Answer 2 · 2026-04-12 04:35:06

290

Views

Enlarging the ring of $S$-integers to get a PID

Published on 12 Apr 2026 - 4:35

score 80 · Answer 3 · 2026-04-15 13:15:26

80

Views

A simple faithful module for $k\langle x,y\rangle/\langle xy-1\rangle$

Published on 15 Apr 2026 - 13:15

score 253 · Answer 4 · 2026-04-12 21:01:40

253

Views

Integral closure of $k[x^3,x^2y,y^3]$ in field of fractions

Published on 12 Apr 2026 - 21:01

score 69 · Answer 5 · 2026-03-26 01:02:40

69

Views

Is there any way to visualize Ring structure using Cayley digraph?

Published on 26 Mar 2026 - 1:02

score 78 · Answer 6 · 2026-05-10 12:31:08

78

Views

Warner "Topological Rings", chapter 1, exercise 3.3

Published on 10 May 2026 - 12:31

score 81 · Answer 7 · 2026-04-13 21:05:24

81

Views

Nillradical is prime ideal, then the ring is not a product ring.

Published on 13 Apr 2026 - 21:05

score 117 · Answer 8 · 2026-05-10 16:57:22

117

Views

Characterization of Injective rings homomorphism from $\mathbb{Z}_m$ to $\mathbb{Z}_n$

Published on 10 May 2026 - 16:57

score 1.1k · Answer 9 · 2026-04-13 14:41:58

1.1k

Views

Basis of ring of algebraic integers and free modules

Published on 13 Apr 2026 - 14:41

score 42 · Answer 10 · 2026-04-12 16:24:50

42

Views

Definition of Polynomial Ring over a field generated by indeterminates.

Published on 12 Apr 2026 - 16:24

score 98 · Answer 11 · 2026-04-11 09:31:44

98

Views

Find the composition of finitely generated module over Dedekind domain

Published on 11 Apr 2026 - 9:31

score 69 · Answer 12 · 2026-04-14 06:45:48

69

Views

Clarification about Quotient Ring Isomorphism Theorem for a Principal Ideal

Published on 14 Apr 2026 - 6:45

score 257 · Answer 13 · 2026-04-17 16:02:12

257

Views

Prove that $J = \{q(x) \in Q[x] \,|\, q(\sqrt{p}) = 0\}$ is a maximal ideal of $\mathbb{Q}[x]$, with p prime

Published on 17 Apr 2026 - 16:02

score 57 · Answer 14 · 2026-04-15 00:23:35

57

Views

Show $f:\mathbb{Z}\to\mathbb{Z}[i]/(3+2i)$ via $c\mapsto c+(3+2i)$ is surjective

Published on 15 Apr 2026 - 0:23

score 29 · Answer 15 · 2026-04-14 13:42:20

29

Views

Is $f(a_1 + p\mathbb{Z},a_2 + p^2 \mathbb{Z}, \ldots) = (0,pa_1 + p^2 \mathbb{Z},\ldots)$ surjective?

Published on 14 Apr 2026 - 13:42

List Question

lcm$(p(x),q(x)) \cdot \gcd(p(x),q(x)) \sim p(x)q(x)$ holds for $D[x]$ with D u.f.d?

Enlarging the ring of $S$-integers to get a PID

A simple faithful module for $k\langle x,y\rangle/\langle xy-1\rangle$

Integral closure of $k[x^3,x^2y,y^3]$ in field of fractions

Is there any way to visualize Ring structure using Cayley digraph?

Warner "Topological Rings", chapter 1, exercise 3.3

Nillradical is prime ideal, then the ring is not a product ring.

Characterization of Injective rings homomorphism from $\mathbb{Z}_m$ to $\mathbb{Z}_n$

Basis of ring of algebraic integers and free modules

Definition of Polynomial Ring over a field generated by indeterminates.

Find the composition of finitely generated module over Dedekind domain

Clarification about Quotient Ring Isomorphism Theorem for a Principal Ideal

Prove that $J = \{q(x) \in Q[x] \,|\, q(\sqrt{p}) = 0\}$ is a maximal ideal of $\mathbb{Q}[x]$, with p prime

Show $f:\mathbb{Z}\to\mathbb{Z}[i]/(3+2i)$ via $c\mapsto c+(3+2i)$ is surjective

Is $f(a_1 + p\mathbb{Z},a_2 + p^2 \mathbb{Z}, \ldots) = (0,pa_1 + p^2 \mathbb{Z},\ldots)$ surjective?

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