Question

Proof Verification: If $R$ is a commutative ring and $I$ an ideal, then $(R/I)^n\cong (R/I)^m$ as $R$-modules iff $n=m$

score 338 · Answer 1 · 2026-04-14 13:33:57

338

Views

Proof Verification: If $R$ is a commutative ring and $I$ an ideal, then $(R/I)^n\cong (R/I)^m$ as $R$-modules iff $n=m$

Published on 14 Apr 2026 - 13:33

score 47 · Answer 2 · 2026-04-12 17:51:40

47

Views

Can someone explain to me what $\mathfrak{p}A_\mathfrak{p}$ means (commutative ring $A$, prime ideal $\mathfrak{p} \triangleleft A$)?

Published on 12 Apr 2026 - 17:51

score 183 · Answer 3 · 2026-04-11 17:27:56

183

Views

Principal Radical Ideal

Published on 11 Apr 2026 - 17:27

score 89 · Answer 4 · 2026-04-19 04:35:47

89

Views

Push-out of localisations of commutative ring

Published on 19 Apr 2026 - 4:35

score 142 · Answer 5 · 2026-04-09 10:08:26

142

Views

Pullback of localisations of commutative ring

Published on 09 Apr 2026 - 10:08

score 152 · Answer 6 · 2026-04-16 15:43:44

152

Views

How to show $1 \otimes x = 0 \in A \otimes B$ implies $x=0$?

Published on 16 Apr 2026 - 15:43

score 97 · Answer 7 · 2026-04-14 18:55:58

97

Views

If $x \in \cap_{n=1}^\infty I^n$, then $x \in xI$.

Published on 14 Apr 2026 - 18:55

score 49 · Answer 8 · 2026-04-24 11:25:02

49

Views

$J(F^n)=0$, where $F$ is an algebraically closed field

Published on 24 Apr 2026 - 11:25

score 129 · Answer 9 · 2026-04-15 21:20:29

129

Views

What is the integral closure of the ring $k[t^3-t, t^2-1]$ in $k(t)$?

Published on 15 Apr 2026 - 21:20

score 395 · Answer 10 · 2026-03-25 16:44:24

395

Views

Over a PID, every submodule of a free module is free

Published on 25 Mar 2026 - 16:44

score 316 · Answer 11 · 2026-05-03 10:24:46

316

Views

Local Cohen-Macaulay ring over which every finitely generated module of finite injective dimension also has finite projective dimension

Published on 03 May 2026 - 10:24

score 49 · Answer 12 · 2026-04-13 07:05:12

49

Views

Atiyah Macdonald; defining a total order on a quotient group $\Gamma$

Published on 13 Apr 2026 - 7:05

score 283 · Answer 13 · 2026-04-15 02:10:28

283

Views

Nakayama's lemma implies isomorphism

Published on 15 Apr 2026 - 2:10

score 47 · Answer 14 · 2026-04-09 04:50:00

47

Views

Some properties of finitely generated ideals in an integral domain

Published on 09 Apr 2026 - 4:50

score 148 · Answer 15 · 2026-04-16 16:00:15

148

Views

The inclusion $\bigcap aM_n\subset a\bigcap M_n$ for descending chains of modules

Published on 16 Apr 2026 - 16:00

List Question

Proof Verification: If $R$ is a commutative ring and $I$ an ideal, then $(R/I)^n\cong (R/I)^m$ as $R$-modules iff $n=m$

Can someone explain to me what $\mathfrak{p}A_\mathfrak{p}$ means (commutative ring $A$, prime ideal $\mathfrak{p} \triangleleft A$)?

Principal Radical Ideal

Push-out of localisations of commutative ring

Pullback of localisations of commutative ring

How to show $1 \otimes x = 0 \in A \otimes B$ implies $x=0$?

If $x \in \cap_{n=1}^\infty I^n$, then $x \in xI$.

$J(F^n)=0$, where $F$ is an algebraically closed field

What is the integral closure of the ring $k[t^3-t, t^2-1]$ in $k(t)$?

Over a PID, every submodule of a free module is free

Local Cohen-Macaulay ring over which every finitely generated module of finite injective dimension also has finite projective dimension

Atiyah Macdonald; defining a total order on a quotient group $\Gamma$

Nakayama's lemma implies isomorphism

Some properties of finitely generated ideals in an integral domain

The inclusion $\bigcap aM_n\subset a\bigcap M_n$ for descending chains of modules

Trending Questions

Popular # Hahtags

Popular Questions