Question

$M$ be a finitely generated module over commutative unital ring $R$ , $N,P$ submodules , $P\subseteq N \subseteq M$ and $M\cong P$ , is $M\cong N$?

score 113 · Answer 1 · 2026-03-25 16:03:43

113

Views

$M$ be a finitely generated module over commutative unital ring $R$ , $N,P$ submodules , $P\subseteq N \subseteq M$ and $M\cong P$ , is $M\cong N$?

Published on 25 Mar 2026 - 16:03

score 135 · Answer 2 · 2026-04-09 23:45:38

135

Views

Chain homotopy and projective complex

Published on 09 Apr 2026 - 23:45

score 169 · Answer 3 · 2016-11-01 03:02:08

169

Views

Showing $R[x]\otimes R[y]\cong R[x,y]$ using certain corollary

Published on 01 Nov 2016 - 3:02

score 126 · Answer 4 · 2026-04-15 20:46:01

126

Views

why $\varphi(J)=(J+I)/I$ and not $J/I$ where $\varphi:R\longrightarrow R/I$?

Published on 15 Apr 2026 - 20:46

score 54 · Answer 5 · 2026-04-11 21:16:15

54

Views

How to get $eA$ faithful from $Ae$ faithful?

Published on 11 Apr 2026 - 21:16

score 1.4k · Answer 6 · 2026-04-14 12:54:10

1.4k

Views

Submodules and the correspondence theorem

Published on 14 Apr 2026 - 12:54

score 866 · Answer 7 · 2026-04-12 11:36:53

866

Views

Understanding the proof that the trivial $\mathbb{C}G$-submodule of $\mathbb{C}G$ is unique.

Published on 12 Apr 2026 - 11:36

score 272 · Answer 8 · 2026-04-15 15:04:52

272

Views

Submodule of an injective $R$-module annihilated by an ideal $I$ of $R$ is an injective $R/I$-module.

Published on 15 Apr 2026 - 15:04

score 291 · Answer 9 · 2026-04-13 08:36:37

291

Views

Counting the number of possible rational canonical forms for a matrix with given minimal polynomial

Published on 13 Apr 2026 - 8:36

score 382 · Answer 10 · 2026-04-14 13:23:40

382

Views

A module with infinitely many associated primes.

Published on 14 Apr 2026 - 13:23

score 652 · Answer 11 · 2026-03-28 05:22:29

652

Views

Show that $M = 0$ iff $M_{\mathfrak{p}} = 0$ iff $M_{\mathfrak{m}} = 0$.

Published on 28 Mar 2026 - 5:22

score 395 · Answer 12 · 2026-04-15 15:37:54

395

Views

Short exact sequence $0 \to A \to B \to C \to 0$ has invariant in $\text{Ext}^1(C,A)$

Published on 15 Apr 2026 - 15:37

score 745 · Answer 13 · 2026-04-13 23:47:51

745

Views

Modules over ring of formal power series

Published on 13 Apr 2026 - 23:47

score 224 · Answer 14 · 2026-04-12 14:32:15

224

Views

Is this module free?

Published on 12 Apr 2026 - 14:32

score 137 · Answer 15 · 2026-04-13 21:42:48

137

Views

Isomorphism between tensor products of abelian groups

Published on 13 Apr 2026 - 21:42

List Question

$M$ be a finitely generated module over commutative unital ring $R$ , $N,P$ submodules , $P\subseteq N \subseteq M$ and $M\cong P$ , is $M\cong N$?

Chain homotopy and projective complex

Showing $R[x]\otimes R[y]\cong R[x,y]$ using certain corollary

why $\varphi(J)=(J+I)/I$ and not $J/I$ where $\varphi:R\longrightarrow R/I$?

How to get $eA$ faithful from $Ae$ faithful?

Submodules and the correspondence theorem

Understanding the proof that the trivial $\mathbb{C}G$-submodule of $\mathbb{C}G$ is unique.

Submodule of an injective $R$-module annihilated by an ideal $I$ of $R$ is an injective $R/I$-module.

Counting the number of possible rational canonical forms for a matrix with given minimal polynomial

A module with infinitely many associated primes.

Show that $M = 0$ iff $M_{\mathfrak{p}} = 0$ iff $M_{\mathfrak{m}} = 0$.

Short exact sequence $0 \to A \to B \to C \to 0$ has invariant in $\text{Ext}^1(C,A)$

Modules over ring of formal power series

Is this module free?

Isomorphism between tensor products of abelian groups

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