Question

Unique factorization domain and principal ideal

score 259 · Answer 1 · 2026-03-25 23:19:16

259

Views

Unique factorization domain and principal ideal

Published on 25 Mar 2026 - 23:19

score 68 · Answer 2 · 2026-04-01 13:45:31

68

Views

Considering $l^\infty(X)$ as a C* algebra, how to show that the maximal ideal is $S(X) = \beta X$

Published on 01 Apr 2026 - 13:45

score 171 · Answer 3 · 2026-03-25 11:09:04

171

Views

Finite dimension quotient ring

Published on 25 Mar 2026 - 11:09

score 67 · Answer 4 · 2026-03-30 20:55:30

67

Views

Show that each of the ideals $I_k=\langle x_1,...,x_k\rangle$ in $F[x_1,...,x_n]$ for $1\leq k \leq n$ are prime and that each power is primary

Published on 30 Mar 2026 - 20:55

score 324 · Answer 5 · 2020-05-09 13:04:19

324

Views

Ring of integers of $K=\mathbb{Q}(\alpha)$ where $\alpha$ is a root of $X^3-3X+1$

Published on 09 May 2020 - 13:04

score 82 · Answer 6 · 2026-03-26 11:01:33

82

Views

Q about 2nd isomorphism Th for rings: Is this true $(S+I)/I\cong S/(S\cap I)\cong S/I$, for subring $S$ and ideal $I$?

Published on 26 Mar 2026 - 11:01

score 87 · Answer 7 · 2020-05-09 18:49:09

87

Views

False proof using Nullstellensatz : Let $J = (S)$ an ideal of polynomials then $\sqrt{S} = \sqrt{J}.$ What's wrong?

Published on 09 May 2020 - 18:49

score 301 · Answer 8 · 2026-03-25 09:25:37

301

Views

Proof that all ideals in a Noetherian ring have a primary decomposition?

Published on 25 Mar 2026 - 9:25

score 216 · Answer 9 · 2020-05-10 13:58:31

216

Views

Is an irreducible ideal always a prime ideal in a finite commutative ring?

Published on 10 May 2020 - 13:58

score 147 · Answer 10 · 2020-05-10 21:54:20

147

Views

What is the radical of this ideal in $\mathbb Q[x,y,z]$?

Published on 10 May 2020 - 21:54

score 364 · Answer 11 · 2026-03-25 10:57:16

364

Views

If in a commutative ring $R$ a maximal ideal is nilpotent, then $R$ is local

Published on 25 Mar 2026 - 10:57

score 165 · Answer 12 · 2020-05-11 17:36:39

165

Views

All ideals of $\mathbb{F}[x]/(f(x))$ in terms of factorization of $f(x)$

Published on 11 May 2020 - 17:36

score 189 · Answer 13 · 2026-03-25 12:55:03

189

Views

What is a generator for an ideal such that $I=\{a+bi|a+b \text{ is even}\}$?

Published on 25 Mar 2026 - 12:55

score 495 · Answer 14 · 2020-05-13 13:06:55

495

Views

Find all ideals of $\mathbb{Z}_n$

Published on 13 May 2020 - 13:06

score 2.7k · Answer 15 · 2026-04-01 10:23:34

2.7k

Views

Show that $\mathbb{Z}[x]/(x)$ is isomorphic to $\mathbb{Z}$

Published on 01 Apr 2026 - 10:23

List Question

Unique factorization domain and principal ideal

Considering $l^\infty(X)$ as a C* algebra, how to show that the maximal ideal is $S(X) = \beta X$

Finite dimension quotient ring

Show that each of the ideals $I_k=\langle x_1,...,x_k\rangle$ in $F[x_1,...,x_n]$ for $1\leq k \leq n$ are prime and that each power is primary

Ring of integers of $K=\mathbb{Q}(\alpha)$ where $\alpha$ is a root of $X^3-3X+1$

Q about 2nd isomorphism Th for rings: Is this true $(S+I)/I\cong S/(S\cap I)\cong S/I$, for subring $S$ and ideal $I$?

False proof using Nullstellensatz : Let $J = (S)$ an ideal of polynomials then $\sqrt{S} = \sqrt{J}.$ What's wrong?

Proof that all ideals in a Noetherian ring have a primary decomposition?

Is an irreducible ideal always a prime ideal in a finite commutative ring?

What is the radical of this ideal in $\mathbb Q[x,y,z]$?

If in a commutative ring $R$ a maximal ideal is nilpotent, then $R$ is local

All ideals of $\mathbb{F}[x]/(f(x))$ in terms of factorization of $f(x)$

What is a generator for an ideal such that $I=\{a+bi|a+b \text{ is even}\}$?

Find all ideals of $\mathbb{Z}_n$

Show that $\mathbb{Z}[x]/(x)$ is isomorphic to $\mathbb{Z}$

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