Question

Prove that two modules are not isomorphic

score 976 · Answer 1 · 2026-04-14 00:33:51

976

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Prove that two modules are not isomorphic

Published on 14 Apr 2026 - 0:33

score 121 · Answer 2 · 2026-04-15 11:38:03

121

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For what values of $a\in \mathbb{Z}[i]$ do $(2,1)$ and $(2+i,a)$ form a basis of $\mathbb{Z}[i]^2$?

Published on 15 Apr 2026 - 11:38

score 748 · Answer 3 · 2026-04-11 20:46:34

748

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Show that the direct sum of countably many $\mathbb{Z}$ copies is not finitely generated

Published on 11 Apr 2026 - 20:46

score 721 · Answer 4 · 2026-04-15 08:44:11

721

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Define a function $\alpha$ :Hom$_R$($R^n,M$) $\rightarrow M^n$ which is a $R$-module isomorphism.

Published on 15 Apr 2026 - 8:44

score 1.5k · Answer 5 · 2026-04-12 01:47:28

1.5k

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Every Submodule of a Free Module is Isomorphic to a Direct Sum of Ideals

Published on 12 Apr 2026 - 1:47

score 47 · Answer 6 · 2026-04-17 01:50:31

47

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Why is $\#X/(F-1)X=|\det_{X\otimes\mathbb{Q}}(F-1)|$, $X$ the character group, $F$ a Frobenius map?

Published on 17 Apr 2026 - 1:50

score 27 · Answer 7 · 2026-04-17 06:46:27

27

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how to prove inverse of a bijective right linear function is right linear?

Published on 17 Apr 2026 - 6:46

score 32 · Answer 8 · 2026-04-12 04:53:28

32

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Can I use $\mathrm{Ext}(A,\,B)\cong\mathbb{Z}/3$ to show two $X\cong X^\ast$?

Published on 12 Apr 2026 - 4:53

score 1.2k · Answer 9 · 2026-04-16 21:08:17

1.2k

Views

Is the dual of a module naturally a comodule?

Published on 16 Apr 2026 - 21:08

score 3.8k · Answer 10 · 2026-04-16 17:06:11

3.8k

Views

Clarification on Proof that any two bases for a free module over certain $R$ have same cardinality

Published on 16 Apr 2026 - 17:06

score 43 · Answer 11 · 2026-04-11 15:00:05

43

Views

Generators of additive subgroup of Dedekind domain

Published on 11 Apr 2026 - 15:00

score 182 · Answer 12 · 2026-04-16 21:52:32

182

Views

Noetherian/Artinian modules

Published on 16 Apr 2026 - 21:52

score 270 · Answer 13 · 2026-04-17 09:39:13

270

Views

Number of conjugacy classes are there over $\mathbb{F}_p$

Published on 17 Apr 2026 - 9:39

score 249 · Answer 14 · 2026-04-16 06:08:55

249

Views

Image of a superfluous module is superfluous

Published on 16 Apr 2026 - 6:08

score 46 · Answer 15 · 2026-03-25 17:45:39

46

Views

Bimodules and Tesnors in TQFT

Published on 25 Mar 2026 - 17:45

List Question

Prove that two modules are not isomorphic

For what values of $a\in \mathbb{Z}[i]$ do $(2,1)$ and $(2+i,a)$ form a basis of $\mathbb{Z}[i]^2$?

Show that the direct sum of countably many $\mathbb{Z}$ copies is not finitely generated

Define a function $\alpha$ :Hom$_R$($R^n,M$) $\rightarrow M^n$ which is a $R$-module isomorphism.

Every Submodule of a Free Module is Isomorphic to a Direct Sum of Ideals

Why is $\#X/(F-1)X=|\det_{X\otimes\mathbb{Q}}(F-1)|$, $X$ the character group, $F$ a Frobenius map?

how to prove inverse of a bijective right linear function is right linear?

Can I use $\mathrm{Ext}(A,\,B)\cong\mathbb{Z}/3$ to show two $X\cong X^\ast$?

Is the dual of a module naturally a comodule?

Clarification on Proof that any two bases for a free module over certain $R$ have same cardinality

Generators of additive subgroup of Dedekind domain

Noetherian/Artinian modules

Number of conjugacy classes are there over $\mathbb{F}_p$

Image of a superfluous module is superfluous

Bimodules and Tesnors in TQFT

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