Question

Extension of $k$-vector space structure to $k[x]$-module structure

score 123 · Answer 1 · 2019-06-12 21:08:04

123

Views

Extension of $k$-vector space structure to $k[x]$-module structure

Published on 12 Jun 2019 - 21:08

score 305 · Answer 2 · 2026-04-01 00:23:44

305

Views

Vector fields as a module over the ring of smooth functions

Published on 01 Apr 2026 - 0:23

score 220 · Answer 3 · 2019-06-13 12:03:08

220

Views

Do we have $a\otimes 1=0$ if and only if $a=0$?

Published on 13 Jun 2019 - 12:03

score 340 · Answer 4 · 2026-04-01 14:20:49

340

Views

Show that there exists a pullback square for modules.

Published on 01 Apr 2026 - 14:20

score 228 · Answer 5 · 2026-03-30 15:37:19

228

Views

Is the category of semimodules over a semiring abelian?

Published on 30 Mar 2026 - 15:37

score 94 · Answer 6 · 2019-06-13 18:21:14

94

Views

show that $M/N$ is a torsion-free module.

Published on 13 Jun 2019 - 18:21

score 131 · Answer 7 · 2026-03-27 04:34:14

131

Views

Localization of a module, thought as localization of a category

Published on 27 Mar 2026 - 4:34

score 365 · Answer 8 · 2026-03-25 19:10:07

365

Views

What is the correct definition of the inverse image functor on sheaves of modules?

Published on 25 Mar 2026 - 19:10

score 35 · Answer 9 · 2026-03-31 11:33:54

35

Views

For ideals of $R$, $I_1, I_2$, Is it true that $(I_1 \cap I_2)M \cong I_1 M \cap I_2 M$ for any $R$-module $M$?

Published on 31 Mar 2026 - 11:33

score 1.5k · Answer 10 · 2026-03-27 00:02:20

1.5k

Views

When does Hom functor commutes with direct sum in the second slot

Published on 27 Mar 2026 - 0:02

score 68 · Answer 11 · 2019-06-16 10:18:47

Let R be a commutative ring with a 1, and let J and K be ideals of R. Prove that $_R(R/J) \cong {_R}(R/K)$ iff $J = K$.

score 912 · Answer 12 · 2026-03-25 06:03:52

912

Views

If $E$ is a finitely generated projective module over a local ring $A$, then $E$ is free: Theorem X.4.4 in Lang's Algebra

Published on 25 Mar 2026 - 6:03

score 70 · Answer 13 · 2019-06-16 18:12:43

70

Views

Solution to linear equation system using modulo 251?

Published on 16 Jun 2019 - 18:12

score 286 · Answer 14 · 2026-03-27 07:24:56

286

Views

Product of simple modules not semi-simple

Published on 27 Mar 2026 - 7:24

score 106 · Answer 15 · 2019-06-16 22:38:03

106

Views

Length of a composition series

Published on 16 Jun 2019 - 22:38

List Question

Extension of $k$-vector space structure to $k[x]$-module structure

Vector fields as a module over the ring of smooth functions

Do we have $a\otimes 1=0$ if and only if $a=0$?

Show that there exists a pullback square for modules.

Is the category of semimodules over a semiring abelian?

show that $M/N$ is a torsion-free module.

Localization of a module, thought as localization of a category

What is the correct definition of the inverse image functor on sheaves of modules?

For ideals of $R$, $I_1, I_2$, Is it true that $(I_1 \cap I_2)M \cong I_1 M \cap I_2 M$ for any $R$-module $M$?

When does Hom functor commutes with direct sum in the second slot

Let R be a commutative ring with a 1, and let J and K be ideals of R. Prove that $_R(R/J) \cong {_R}(R/K)$ iff $J = K$.

If $E$ is a finitely generated projective module over a local ring $A$, then $E$ is free: Theorem X.4.4 in Lang's Algebra

Solution to linear equation system using modulo 251?

Product of simple modules not semi-simple

Length of a composition series

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