Question

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

score 51 · Answer 1 · 2026-04-20 03:53:27

51

Views

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

Published on 20 Apr 2026 - 3:53

score 121 · Answer 2 · 2026-04-13 01:39:52

121

Views

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

Published on 13 Apr 2026 - 1:39

score 109 · Answer 3 · 2026-04-12 01:25:09

109

Views

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

Published on 12 Apr 2026 - 1:25

score 303 · Answer 4 · 2026-04-04 21:02:55

303

Views

Correspondence Theorem for Lie algebras

Published on 04 Apr 2026 - 21:02

score 660 · Answer 5 · 2026-04-15 19:50:31

660

Views

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

Published on 15 Apr 2026 - 19:50

score 117 · Answer 6 · 2026-03-25 14:22:07

117

Views

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

Published on 25 Mar 2026 - 14:22

score 54 · Answer 7 · 2026-05-10 09:51:51

54

Views

$R$-module homomorphism

Published on 10 May 2026 - 9:51

score 37 · Answer 8 · 2026-03-25 12:49:46

37

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 25 Mar 2026 - 12:49

score 295 · Answer 9 · 2026-03-25 14:23:55

295

Views

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

Published on 25 Mar 2026 - 14:23

score 113 · Answer 10 · 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 27 · Answer 11 · 2026-03-25 15:59:21

27

Views

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

Published on 25 Mar 2026 - 15:59

score 63 · Answer 12 · 2026-04-10 20:55:52

63

Views

How to denote isomorphism/ ring direct product

Published on 10 Apr 2026 - 20:55

score 436 · Answer 13 · 2026-03-25 12:50:20

436

Views

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

Published on 25 Mar 2026 - 12:50

score 168 · Answer 14 · 2026-03-25 14:20:52

168

Views

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

Published on 25 Mar 2026 - 14:20

score 75 · Answer 15 · 2026-03-25 14:22:37

75

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 25 Mar 2026 - 14:22

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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