Question

Show that $y-x^2 \notin \langle x(x-1), (x-1)y\rangle$ in $\mathbb{C}[x,y]$

score 74 · Answer 1 · 2026-04-14 21:30:08

74

Views

Show that $y-x^2 \notin \langle x(x-1), (x-1)y\rangle$ in $\mathbb{C}[x,y]$

Published on 14 Apr 2026 - 21:30

score 68 · Answer 2 · 2026-04-15 06:33:15

68

Views

Is it true that $\mathbb Z[x_1, \ldots, x_n] / \mathcal P \simeq (\mathbb Z/ p) [ x_1, \ldots, x_n]$?

Published on 15 Apr 2026 - 6:33

score 42 · Answer 3 · 2026-04-14 05:11:59

42

Views

$A[x]$ is a commutative domain if and only if $A$ is a commutative domain

Published on 14 Apr 2026 - 5:11

score 105 · Answer 4 · 2026-04-13 00:29:18

105

Views

Irreducibility of Polynomials without Eisenstein

Published on 13 Apr 2026 - 0:29

score 34 · Answer 5 · 2026-04-16 00:57:42

34

Views

Let the set $S=\{f \in C[a,b] : f(x)=0 \forall x \in [c,d]\}$ in $C[a,b]$

Published on 16 Apr 2026 - 0:57

score 202 · Answer 6 · 2026-04-14 16:23:01

202

Views

Terminology Question: "Local Module" : Modules with a unique maximal submodule.

Published on 14 Apr 2026 - 16:23

score 139 · Answer 7 · 2026-04-13 22:47:40

139

Views

Show RxZ is a Ring with 1

Published on 13 Apr 2026 - 22:47

score 297 · Answer 8 · 2026-04-12 14:30:12

297

Views

Why "every element is a divisor of zero in any ring of polynomials" is false?

Published on 12 Apr 2026 - 14:30

score 52 · Answer 9 · 2026-04-16 06:44:24

Show that $P$ is prime iff the following holds: For any $A\in \mathcal P\left(S\right)$ either $A\in P$ or $A^{c}=S\setminus A\in P$ but not both.

score 383 · Answer 10 · 2026-04-12 07:28:41

383

Views

Sum of endomorphisms that is not an endomorphism

Published on 12 Apr 2026 - 7:28

score 1.1k · Answer 11 · 2026-04-16 06:05:45

1.1k

Views

Show that any ideal in $\mathbb{C}[x,y]$ containing $y$ can be generated by $2$ elements

Published on 16 Apr 2026 - 6:05

score 128 · Answer 12 · 2026-04-17 12:44:44

128

Views

Quick question on polynomial notation (from the perspective of rings)

Published on 17 Apr 2026 - 12:44

score 234 · Answer 13 · 2026-04-09 23:25:39

234

Views

Generators of a maximal ideal

Published on 09 Apr 2026 - 23:25

score 146 · Answer 14 · 2026-05-15 00:38:43

146

Views

Two definitions for regular rings

Published on 15 May 2026 - 0:38

score 481 · Answer 15 · 2026-04-14 05:07:47

481

Views

Polynomial division modulo 5, gcd of two polynomials

Published on 14 Apr 2026 - 5:07

List Question

Show that $y-x^2 \notin \langle x(x-1), (x-1)y\rangle$ in $\mathbb{C}[x,y]$

Is it true that $\mathbb Z[x_1, \ldots, x_n] / \mathcal P \simeq (\mathbb Z/ p) [ x_1, \ldots, x_n]$?

$A[x]$ is a commutative domain if and only if $A$ is a commutative domain

Irreducibility of Polynomials without Eisenstein

Let the set $S=\{f \in C[a,b] : f(x)=0 \forall x \in [c,d]\}$ in $C[a,b]$

Terminology Question: "Local Module" : Modules with a unique maximal submodule.

Show RxZ is a Ring with 1

Why "every element is a divisor of zero in any ring of polynomials" is false?

Show that $P$ is prime iff the following holds: For any $A\in \mathcal P\left(S\right)$ either $A\in P$ or $A^{c}=S\setminus A\in P$ but not both.

Sum of endomorphisms that is not an endomorphism

Show that any ideal in $\mathbb{C}[x,y]$ containing $y$ can be generated by $2$ elements

Quick question on polynomial notation (from the perspective of rings)

Generators of a maximal ideal

Two definitions for regular rings

Polynomial division modulo 5, gcd of two polynomials

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