Question

Question about defining a free module over an arbitrary set.

score 57 · Answer 1 · 2019-12-22 06:41:43

57

Views

Question about defining a free module over an arbitrary set.

Published on 22 Dec 2019 - 6:41

score 43 · Answer 2 · 2026-03-27 17:51:55

43

Views

confusion regarding direct sum of modules

Published on 27 Mar 2026 - 17:51

score 336 · Answer 3 · 2019-12-23 23:47:12

336

Views

If $R$ has zero divisors and $M$ is an $R$ module, is every element of $M$ torsion?

Published on 23 Dec 2019 - 23:47

score 55 · Answer 4 · 2026-03-27 17:50:26

55

Views

Basic confusion regarding tensor product

Published on 27 Mar 2026 - 17:50

score 137 · Answer 5 · 2019-12-24 10:38:40

137

Views

Isomorphism of $A$-modules

Published on 24 Dec 2019 - 10:38

score 78 · Answer 6 · 2026-02-23 06:36:25

78

Views

Is there an upper bound for $2^x \bmod P$ in range again?

Published on 23 Feb 2026 - 6:36

score 104 · Answer 7 · 2019-12-25 13:08:17

104

Views

Is $A \otimes _R R$ isomorphic to $A$ even when $R$ does not have an identity?

Published on 25 Dec 2019 - 13:08

score 78 · Answer 8 · 2026-02-23 02:40:44

78

Views

Can the division rings appearing in the Wedderburn-Artin theorem be isomorphic?

Published on 23 Feb 2026 - 2:40

score 65 · Answer 9 · 2019-12-25 14:28:40

65

Views

Finding generators of the $R$-module $\hom_{R}(\Bbb{Z}[y,z]/(y^2-1,z^2-1),\Bbb C^\times)$

Published on 25 Dec 2019 - 14:28

score 62 · Answer 10 · 2026-03-27 22:00:39

62

Views

$\operatorname{Hom}_A(A^*, P)\cong P$ such that $P$ is projective under the given assumption?

Published on 27 Mar 2026 - 22:00

score 111 · Answer 11 · 2019-12-27 00:10:27

111

Views

For simple $R$-modules, $A$,$B$, and $C$ if $A\oplus C\cong B\oplus C$ as $R$-modules then $A\cong B$ as $R$-modules.

Published on 27 Dec 2019 - 0:10

score 101 · Answer 12 · 2026-03-26 02:53:41

101

Views

Example of $S$-Noetherian rings

Published on 26 Mar 2026 - 2:53

score 94 · Answer 13 · 2026-03-26 14:42:54

94

Views

Necessary and sufficient condition of $S$-Noetherian rings

Published on 26 Mar 2026 - 14:42

score 88 · Answer 14 · 2026-03-30 08:31:25

88

Views

Prove $\{(2,0)\}$ is not extendable to a basis for $\mathbb{Z}^2$

Published on 30 Mar 2026 - 8:31

score 49 · Answer 15 · 2019-12-30 00:19:22

49

Views

Examples of modules satisfying $(0:_{M/N}r):=\{m+N\in M/N:r(m+N)\in N\}=\{m\in M:rm\in N\}=(N:_{M}r)$

Published on 30 Dec 2019 - 0:19

List Question

Question about defining a free module over an arbitrary set.

confusion regarding direct sum of modules

If $R$ has zero divisors and $M$ is an $R$ module, is every element of $M$ torsion?

Basic confusion regarding tensor product

Isomorphism of $A$-modules

Is there an upper bound for $2^x \bmod P$ in range again?

Is $A \otimes _R R$ isomorphic to $A$ even when $R$ does not have an identity?

Can the division rings appearing in the Wedderburn-Artin theorem be isomorphic?

Finding generators of the $R$-module $\hom_{R}(\Bbb{Z}[y,z]/(y^2-1,z^2-1),\Bbb C^\times)$

$\operatorname{Hom}_A(A^*, P)\cong P$ such that $P$ is projective under the given assumption?

For simple $R$-modules, $A$,$B$, and $C$ if $A\oplus C\cong B\oplus C$ as $R$-modules then $A\cong B$ as $R$-modules.

Example of $S$-Noetherian rings

Necessary and sufficient condition of $S$-Noetherian rings

Prove $\{(2,0)\}$ is not extendable to a basis for $\mathbb{Z}^2$

Examples of modules satisfying $(0:_{M/N}r):=\{m+N\in M/N:r(m+N)\in N\}=\{m\in M:rm\in N\}=(N:_{M}r)$

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