Question

If $M=f(N)\oplus K$, then there is a left inverse to $f$

score 122 · Answer 1 · 2018-04-21 02:36:15

122

Views

If $M=f(N)\oplus K$, then there is a left inverse to $f$

Published on 21 Apr 2018 - 2:36

score 332 · Answer 2 · 2018-04-21 03:25:46

332

Views

The basic property of Tor functor.

Published on 21 Apr 2018 - 3:25

score 73 · Answer 3 · 2026-03-25 11:05:12

73

Views

Prove that $f(N)$ is a direct summand

Published on 25 Mar 2026 - 11:05

score 49 · Answer 4 · 2026-03-25 09:50:19

49

Views

If $f'\circ f=\operatorname{id}_N$, then $f(N)$ is a direct summand

Published on 25 Mar 2026 - 9:50

score 152 · Answer 5 · 2018-04-21 15:23:43

152

Views

Isomorphism of $F$-algebras

Published on 21 Apr 2018 - 15:23

score 551 · Answer 6 · 2026-03-25 06:22:11

551

Views

If the $R$-module $M$ is finitely generated, but some generating set is not linearly independent, is $M$ not free?

Published on 25 Mar 2026 - 6:22

score 50 · Answer 7 · 2018-04-21 23:41:39

50

Views

Inclusion between submodules

Published on 21 Apr 2018 - 23:41

score 105 · Answer 8 · 2026-03-25 11:00:48

105

Views

When abelian subgroup is direct summand?

Published on 25 Mar 2026 - 11:00

score 1.6k · Answer 9 · 2026-03-26 06:06:48

1.6k

Views

Examples of interesting rings to study during an undergraduate course in non-commutative rings.

Published on 26 Mar 2026 - 6:06

score 450 · Answer 10 · 2018-04-24 00:45:03

450

Views

What is $ \operatorname{Hom}_{k[x]}(k[x]/\langle x^2 \rangle , k[x]/ \langle x^3 \rangle ) $, where $ k $ is a field?

Published on 24 Apr 2018 - 0:45

score 162 · Answer 11 · 2018-04-24 14:12:51

162

Views

Dauns’ Proposition 3-4.5 (i) on essential extensions

Published on 24 Apr 2018 - 14:12

score 428 · Answer 12 · 2018-04-24 14:24:10

428

Views

What $2\mathbb Z/4\mathbb Z$ is not flat module in the ring $\mathbb Z/4\mathbb Z$

Published on 24 Apr 2018 - 14:24

score 40 · Answer 13 · 2026-03-22 07:24:38

40

Views

Algebra-module over a set, is there such a thing?

Published on 22 Mar 2026 - 7:24

score 234 · Answer 14 · 2026-03-26 11:01:30

234

Views

Let R be a ring with 1. Show that every principal left ideal is generated by an idempotent iff it is a direct summand of ${}_{R}R$

Published on 26 Mar 2026 - 11:01

score 385 · Answer 15 · 2026-03-22 16:53:15

385

Views

Question about Hopkins-Levitzki Theorem's proof

Published on 22 Mar 2026 - 16:53

List Question

If $M=f(N)\oplus K$, then there is a left inverse to $f$

The basic property of Tor functor.

Prove that $f(N)$ is a direct summand

If $f'\circ f=\operatorname{id}_N$, then $f(N)$ is a direct summand

Isomorphism of $F$-algebras

If the $R$-module $M$ is finitely generated, but some generating set is not linearly independent, is $M$ not free?

Inclusion between submodules

When abelian subgroup is direct summand?

Examples of interesting rings to study during an undergraduate course in non-commutative rings.

What is $ \operatorname{Hom}_{k[x]}(k[x]/\langle x^2 \rangle , k[x]/ \langle x^3 \rangle ) $, where $ k $ is a field?

Dauns’ Proposition 3-4.5 (i) on essential extensions

What $2\mathbb Z/4\mathbb Z$ is not flat module in the ring $\mathbb Z/4\mathbb Z$

Algebra-module over a set, is there such a thing?

Let R be a ring with 1. Show that every principal left ideal is generated by an idempotent iff it is a direct summand of ${}_{R}R$

Question about Hopkins-Levitzki Theorem's proof

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