Question

Does the isomorphism $\text{Ann}^M(1-ab)\cong \left(\text{Ann}^M(1-ab)\right)a$ always hold?

score 49 · Answer 1 · 2020-03-31 18:38:45

49

Views

Does the isomorphism $\text{Ann}^M(1-ab)\cong \left(\text{Ann}^M(1-ab)\right)a$ always hold?

Published on 31 Mar 2020 - 18:38

score 120 · Answer 2 · 2020-04-06 00:08:29

120

Views

Example of a non-isomorphic map from $D^{-1}R$-modules

Published on 06 Apr 2020 - 0:08

score 108 · Answer 3 · 2020-04-06 01:05:30

108

Views

$Hom_R(R,R/I)$ isomorphic to R/I as R-modules

Published on 06 Apr 2020 - 1:05

score 302 · Answer 4 · 2020-04-25 18:34:06

302

Views

Correspondence Theorem for Lie algebras

Published on 25 Apr 2020 - 18:34

score 657 · Answer 5 · 2020-05-03 22:39:21

657

Views

A module homomorphism is injective iff the kernel is isomorphic to the trivial module

Published on 03 May 2020 - 22:39

score 116 · Answer 6 · 2020-06-27 16:15:05

116

Views

Why $M/\mathfrak{a}M \oplus M/\mathfrak{b}M \simeq M/(\mathfrak{a \cap b})M$?

Published on 27 Jun 2020 - 16:15

score 51 · Answer 7 · 2020-07-06 19:33:29

51

Views

$R$-module homomorphism

Published on 06 Jul 2020 - 19:33

score 36 · Answer 8 · 2020-07-11 12:02:20

36

Views

If $f_x$ is injective whenever it is surjective on $M$, then is $f_x$ injective whenever it is surjective on $\bigoplus_{i\in \Bbb N}M$?

Published on 11 Jul 2020 - 12:02

score 294 · Answer 9 · 2020-07-12 18:36:10

294

Views

Proving that $0 \rightarrow \Bbb Z \rightarrow \Bbb Q \rightarrow \Bbb Q / \Bbb Z \rightarrow 0$ does not split.

Published on 12 Jul 2020 - 18:36

score 112 · Answer 10 · 2016-10-31 08:15:01

112

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 31 Oct 2016 - 8:15

score 26 · Answer 11 · 2017-02-12 15:51:12

26

Views

Modules where $A+(M/A) \ncong A\oplus M/A$

Published on 12 Feb 2017 - 15:51

score 60 · Answer 12 · 2017-02-16 15:37:38

60

Views

How to denote isomorphism/ ring direct product

Published on 16 Feb 2017 - 15:37

score 435 · Answer 13 · 2017-03-03 21:03:00

435

Views

The set of all covectors fields and the dual to the set of all vector fields, isomorphic?

Published on 03 Mar 2017 - 21:03

score 167 · Answer 14 · 2017-03-09 08:22:42

167

Views

Show $\phi(B)/\phi(A)\cong B/A\oplus(B\cap\ker\phi)$

Published on 09 Mar 2017 - 8:22

score 74 · Answer 15 · 2023-02-04 00:21:46

74

Views

For groups, rings, or $R$-modules $A, B, C$ with $C\subseteq B$, does $A/B \cong A/C$ imply that $B=C$?

Published on 04 Feb 2023 - 0:21

List Question

Does the isomorphism $\text{Ann}^M(1-ab)\cong \left(\text{Ann}^M(1-ab)\right)a$ always hold?

Example of a non-isomorphic map from $D^{-1}R$-modules

$Hom_R(R,R/I)$ isomorphic to R/I as R-modules

Correspondence Theorem for Lie algebras

A module homomorphism is injective iff the kernel is isomorphic to the trivial module

Why $M/\mathfrak{a}M \oplus M/\mathfrak{b}M \simeq M/(\mathfrak{a \cap b})M$?

$R$-module homomorphism

If $f_x$ is injective whenever it is surjective on $M$, then is $f_x$ injective whenever it is surjective on $\bigoplus_{i\in \Bbb N}M$?

Proving that $0 \rightarrow \Bbb Z \rightarrow \Bbb Q \rightarrow \Bbb Q / \Bbb Z \rightarrow 0$ does not split.

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

Modules where $A+(M/A) \ncong A\oplus M/A$

How to denote isomorphism/ ring direct product

The set of all covectors fields and the dual to the set of all vector fields, isomorphic?

Show $\phi(B)/\phi(A)\cong B/A\oplus(B\cap\ker\phi)$

For groups, rings, or $R$-modules $A, B, C$ with $C\subseteq B$, does $A/B \cong A/C$ imply that $B=C$?

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