Question

If $N \leq M$ and $Rad(M/N)=\{ 0\}$ then $Rad(M)\subseteq N$

score 52 · Answer 1 · 2026-04-16 05:28:49

If $N \leq M$ and $Rad(M/N)=\{ 0\}$ then $Rad(M)\subseteq N$

Published on 16 Apr 2026 - 5:28

score 49 · Answer 2 · 2026-04-13 11:21:18

How the map in proving the direct limit property $\lim\limits_{\to}(M_i\times N)\cong(\lim\limits_{\to}M_i)\times N$ is well defined

score 82 · Answer 3 · 2026-04-13 20:03:42

82

Views

Existence of a matrix from a Euclidean domain

Published on 13 Apr 2026 - 20:03

score 92 · Answer 4 · 2026-04-13 00:23:30

92

Views

Extending a bilinear map $f:U\times V\rightarrow W$ to a unique homomorphism $f_1 :A\rightarrow W$.

Published on 13 Apr 2026 - 0:23

score 59 · Answer 5 · 2026-04-10 00:04:47

59

Views

What are the invariant factors of a matrix?

Published on 10 Apr 2026 - 0:04

score 49 · Answer 6 · 2026-04-15 05:56:31

49

Views

About superfluous epimorphism in exact rows between R modules [Ker g is superfluous submodule]

Published on 15 Apr 2026 - 5:56

score 89 · Answer 7 · 2026-04-15 20:11:23

89

Views

A Ring with Rank Condition that doesn't satisfy Strong Rank Condition

Published on 15 Apr 2026 - 20:11

score 164 · Answer 8 · 2026-04-16 06:28:24

164

Views

Question on a (presumably) basic $O_X$-module isomorphism

Published on 16 Apr 2026 - 6:28

score 74 · Answer 9 · 2026-04-16 12:42:16

74

Views

$Hom \left(\bigoplus_{i=1}^n M_i,\bigoplus_{j=1}^m N_j \right) \cong \bigoplus_{i,j}Hom(M_i,N_j)$

Published on 16 Apr 2026 - 12:42

score 125 · Answer 10 · 2026-04-11 00:46:17

125

Views

Module with exactly one maximal submodule not local

Published on 11 Apr 2026 - 0:46

score 204 · Answer 11 · 2026-04-09 10:15:28

204

Views

Socle series and radical series have same length

Published on 09 Apr 2026 - 10:15

score 52 · Answer 12 · 2026-04-16 14:23:17

If $K \subseteq^{\mathrm{ess}} N \subseteq M$ implies $N/K$ is f.cog for all $N,K$ , then is $M/A$ f.cog for any $A \supseteq \mathrm{soc}(M)$?

score 181 · Answer 13 · 2026-04-14 21:02:55

181

Views

Showing that $\varinjlim (L_i \otimes M_i) \cong \varinjlim L_i \otimes \varinjlim M_i$

Published on 14 Apr 2026 - 21:02

score 36 · Answer 14 · 2026-04-09 09:55:57

36

Views

An endomorphism ring acting on a module from the right

Published on 09 Apr 2026 - 9:55

score 40 · Answer 15 · 2026-04-16 20:56:36

40

Views

radical and composition series

Published on 16 Apr 2026 - 20:56

List Question

If $N \leq M$ and $Rad(M/N)=\{ 0\}$ then $Rad(M)\subseteq N$

How the map in proving the direct limit property $\lim\limits_{\to}(M_i\times N)\cong(\lim\limits_{\to}M_i)\times N$ is well defined

Existence of a matrix from a Euclidean domain

Extending a bilinear map $f:U\times V\rightarrow W$ to a unique homomorphism $f_1 :A\rightarrow W$.

What are the invariant factors of a matrix?

About superfluous epimorphism in exact rows between R modules [Ker g is superfluous submodule]

A Ring with Rank Condition that doesn't satisfy Strong Rank Condition

Question on a (presumably) basic $O_X$-module isomorphism

$Hom \left(\bigoplus_{i=1}^n M_i,\bigoplus_{j=1}^m N_j \right) \cong \bigoplus_{i,j}Hom(M_i,N_j)$

Module with exactly one maximal submodule not local

Socle series and radical series have same length

If $K \subseteq^{\mathrm{ess}} N \subseteq M$ implies $N/K$ is f.cog for all $N,K$ , then is $M/A$ f.cog for any $A \supseteq \mathrm{soc}(M)$?

Showing that $\varinjlim (L_i \otimes M_i) \cong \varinjlim L_i \otimes \varinjlim M_i$

An endomorphism ring acting on a module from the right

radical and composition series

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