Question

Show $\mathbb{Z}/p\mathbb{Z}\otimes_\mathbb{Z}\mathbb{Z}/q\mathbb{Z}=\{0\}$ if $p\not=q$ "explicitly", without theorems

score 79 · Answer 1 · 2026-04-12 16:18:38

79

Views

Show $\mathbb{Z}/p\mathbb{Z}\otimes_\mathbb{Z}\mathbb{Z}/q\mathbb{Z}=\{0\}$ if $p\not=q$ "explicitly", without theorems

Published on 12 Apr 2026 - 16:18

score 61 · Answer 2 · 2026-04-14 11:53:48

61

Views

The equivalence of two definitions of the radical of the morphisms

Published on 14 Apr 2026 - 11:53

score 73 · Answer 3 · 2026-04-16 17:40:17

73

Views

What is the rank of the module $\mathbb F_p[[x,y]]$ over its subring $\mathbb F_p[[x^{p^m},y^{p^n}]]$?

Published on 16 Apr 2026 - 17:40

score 156 · Answer 4 · 2026-04-12 19:24:47

156

Views

Is a finitely generated and globally generated $\mathcal{O}_X$-module over non-quasicompact $X$ always not finitely globally generated?

Published on 12 Apr 2026 - 19:24

score 83 · Answer 5 · 2026-04-17 00:19:35

83

Views

$M/\mathfrak{m}M\cong N/\mathfrak{m}N$ implies that $M\cong N$

Published on 17 Apr 2026 - 0:19

score 146 · Answer 6 · 2026-04-14 20:49:51

146

Views

Need help showing that the only submodules of $M$ are the ones in an ascending chain.

Published on 14 Apr 2026 - 20:49

score 165 · Answer 7 · 2026-04-16 09:58:06

165

Views

Tensor product of simple $sl_2$ modules

Published on 16 Apr 2026 - 9:58

score 78 · Answer 8 · 2026-04-14 14:36:01

78

Views

Trouble understanding this paragraph on projective modules

Published on 14 Apr 2026 - 14:36

score 48 · Answer 9 · 2026-04-12 22:46:28

48

Views

Confusion on the tensor product $I\otimes_A A/I$

Published on 12 Apr 2026 - 22:46

score 71 · Answer 10 · 2026-04-11 21:36:53

71

Views

Are module finite algebras over Noetherian semiperfect rings again semiperfect?

Published on 11 Apr 2026 - 21:36

score 87 · Answer 11 · 2026-04-11 14:46:01

87

Views

Annihilator as a maximal ideal

Published on 11 Apr 2026 - 14:46

score 87 · Answer 12 · 2026-04-13 23:07:18

87

Views

Example of non-torsion Artinian module over non-domain is not Noetherian module

Published on 13 Apr 2026 - 23:07

score 149 · Answer 13 · 2026-03-26 20:41:10

149

Views

The injective hull of the ring of all eventually constant sequences of elements of $\mathbb{Z}_2$

Published on 26 Mar 2026 - 20:41

score 37 · Answer 14 · 2026-04-09 20:57:59

37

Views

Homomorphism from a simple module to a direct sum of itself

Published on 09 Apr 2026 - 20:57

score 75 · Answer 15 · 2026-04-12 09:57:17

75

Views

About Jacobson's proof of the structure theorem for f.g. modules over a PID

Published on 12 Apr 2026 - 9:57

List Question

Show $\mathbb{Z}/p\mathbb{Z}\otimes_\mathbb{Z}\mathbb{Z}/q\mathbb{Z}=\{0\}$ if $p\not=q$ "explicitly", without theorems

The equivalence of two definitions of the radical of the morphisms

What is the rank of the module $\mathbb F_p[[x,y]]$ over its subring $\mathbb F_p[[x^{p^m},y^{p^n}]]$?

Is a finitely generated and globally generated $\mathcal{O}_X$-module over non-quasicompact $X$ always not finitely globally generated?

$M/\mathfrak{m}M\cong N/\mathfrak{m}N$ implies that $M\cong N$

Need help showing that the only submodules of $M$ are the ones in an ascending chain.

Tensor product of simple $sl_2$ modules

Trouble understanding this paragraph on projective modules

Confusion on the tensor product $I\otimes_A A/I$

Are module finite algebras over Noetherian semiperfect rings again semiperfect?

Annihilator as a maximal ideal

Example of non-torsion Artinian module over non-domain is not Noetherian module

The injective hull of the ring of all eventually constant sequences of elements of $\mathbb{Z}_2$

Homomorphism from a simple module to a direct sum of itself

About Jacobson's proof of the structure theorem for f.g. modules over a PID

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