Question

On subring $R\subseteq S$ such that the inclusion map $i: R\to S$ splits as an $R$-module map

score 321 · Answer 1 · 2026-03-27 03:43:21

321

Views

On subring $R\subseteq S$ such that the inclusion map $i: R\to S$ splits as an $R$-module map

Published on 27 Mar 2026 - 3:43

score 1.1k · Answer 2 · 2026-04-15 08:50:41

1.1k

Views

Let $R$ be a commutative ring with $1 \neq 0$. Show that if $I$ is a prime ideal, then $R/I$ is an integral domain.

Published on 15 Apr 2026 - 8:50

score 315 · Answer 3 · 2026-03-25 21:49:57

315

Views

Isomorphism from $Z[i]/(p)$ to $(p^n)/(p^{n+1})$ where $p$ is a irreducible element .

Published on 25 Mar 2026 - 21:49

score 41 · Answer 4 · 2026-04-15 20:43:29

41

Views

Definition of irreducible - inclusive or exclusive or?

Published on 15 Apr 2026 - 20:43

score 70 · Answer 5 · 2026-04-14 12:14:57

70

Views

Can a commutative ring $R$ with identity be isomorphic to the product ring $R\times R$?

Published on 14 Apr 2026 - 12:14

score 551 · Answer 6 · 2026-03-25 23:42:42

551

Views

How to determine the local ring $\mathcal{O}_{X,p}$ of the variety $X=V(xy)\subset\mathbb{A}^2$ at $p=(0,0)$.

Published on 25 Mar 2026 - 23:42

score 324 · Answer 7 · 2026-05-10 20:39:26

324

Views

Is $\frac{\mathbb{Z}[X,Y]}{(2, X)}$ a Euclidean Domain?

Published on 10 May 2026 - 20:39

score 80 · Answer 8 · 2026-04-12 16:07:08

80

Views

Is $\zeta(-1)=0$ in the empty topological space?

Published on 12 Apr 2026 - 16:07

score 63 · Answer 9 · 2026-04-15 00:53:22

63

Views

Is $\mathbb{Z}_3[x] / \langle x^2+x+1 \rangle $ an integral domain?

Published on 15 Apr 2026 - 0:53

score 380 · Answer 10 · 2026-04-12 11:07:23

380

Views

Show that any non zero ideal of a principal ideal domain is a unique product of prime ideals

Published on 12 Apr 2026 - 11:07

score 31 · Answer 11 · 2026-04-16 14:05:45

31

Views

Does the finiteness of $R/P$ imply that of $R/P^r$, where $P$ is a prime ideal?

Published on 16 Apr 2026 - 14:05

score 191 · Answer 12 · 2026-04-12 01:58:23

191

Views

Is the order of a ray class group bounded by the class number?

Published on 12 Apr 2026 - 1:58

score 142 · Answer 13 · 2026-04-14 03:07:09

142

Views

$R$ is a Noetherian ring if and only if both $I$ and $J$ are Noetherian $R$-modules, where $I,J$ are distinct maximal ideals

Published on 14 Apr 2026 - 3:07

score 194 · Answer 14 · 2026-05-11 08:42:05

194

Views

$f(x),g(x)$ co-prime in $R[X]$ with $R$ a UFD implies $f(x), g(x) $ co-prime in $\operatorname{Frac}(R)[X]$

Published on 11 May 2026 - 8:42

score 31 · Answer 15 · 2026-04-16 14:26:39

31

Views

Find $c(x,y), d(x,y) \in F[x,y]$ such that $a(x,y)c(x,y) + b(x,y)d(x,y)$ is a non-zero polynomial in $F[X]$

Published on 16 Apr 2026 - 14:26

List Question

On subring $R\subseteq S$ such that the inclusion map $i: R\to S$ splits as an $R$-module map

Let $R$ be a commutative ring with $1 \neq 0$. Show that if $I$ is a prime ideal, then $R/I$ is an integral domain.

Isomorphism from $Z[i]/(p)$ to $(p^n)/(p^{n+1})$ where $p$ is a irreducible element .

Definition of irreducible - inclusive or exclusive or?

Can a commutative ring $R$ with identity be isomorphic to the product ring $R\times R$?

How to determine the local ring $\mathcal{O}_{X,p}$ of the variety $X=V(xy)\subset\mathbb{A}^2$ at $p=(0,0)$.

Is $\frac{\mathbb{Z}[X,Y]}{(2, X)}$ a Euclidean Domain?

Is $\zeta(-1)=0$ in the empty topological space?

Is $\mathbb{Z}_3[x] / \langle x^2+x+1 \rangle $ an integral domain?

Show that any non zero ideal of a principal ideal domain is a unique product of prime ideals

Does the finiteness of $R/P$ imply that of $R/P^r$, where $P$ is a prime ideal?

Is the order of a ray class group bounded by the class number?

$R$ is a Noetherian ring if and only if both $I$ and $J$ are Noetherian $R$-modules, where $I,J$ are distinct maximal ideals

$f(x),g(x)$ co-prime in $R[X]$ with $R$ a UFD implies $f(x), g(x) $ co-prime in $\operatorname{Frac}(R)[X]$

Find $c(x,y), d(x,y) \in F[x,y]$ such that $a(x,y)c(x,y) + b(x,y)d(x,y)$ is a non-zero polynomial in $F[X]$

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