Question

Are these approaches for proving that a function is well-defined the same?

score 106 · Answer 1 · 2026-04-10 19:13:28

106

Views

Are these approaches for proving that a function is well-defined the same?

Published on 10 Apr 2026 - 19:13

score 22 · Answer 2 · 2026-04-16 21:08:21

22

Views

$R$-algebras and the tensor-algebra.

Published on 16 Apr 2026 - 21:08

score 45 · Answer 3 · 2026-04-14 11:02:50

45

Views

Is this Proof of Well-definedness Correct?

Published on 14 Apr 2026 - 11:02

score 52 · Answer 4 · 2026-04-11 12:05:00

52

Views

Is the inverse of a finitely generated $A$-submodule of $\mathrm{Frac}(A)$ still finitely generated?

Published on 11 Apr 2026 - 12:05

score 15 · Answer 5 · 2026-03-25 17:43:58

15

Views

Show that the statements about module $M_R$ are equivalent.

Published on 25 Mar 2026 - 17:43

score 68 · Answer 6 · 2026-04-15 09:04:46

68

Views

Must I Prove Exactness at these Points as Well?

Published on 15 Apr 2026 - 9:04

score 80 · Answer 7 · 2026-04-13 22:11:47

80

Views

tensor product of modules over tensor product

Published on 13 Apr 2026 - 22:11

score 34 · Answer 8 · 2026-03-25 17:37:19

34

Views

cyclic $R$-module correspondence in $R$ which is PID

Published on 25 Mar 2026 - 17:37

score 134 · Answer 9 · 2026-04-16 21:57:48

134

Views

Proof of $\operatorname{rank}(M) = \operatorname{rank}(M/\operatorname{Tor}(M))$

Published on 16 Apr 2026 - 21:57

score 28 · Answer 10 · 2026-04-12 19:22:54

Unique $R$-algebra homomorphism from the exterior algebra to an $R$-algebra $A$, if $a^2 = 0$ for all $a \in A$.

score 51 · Answer 11 · 2026-04-15 06:37:19

51

Views

Is there a way to determine when an abelian group $(M,+)$ admits a $R[G]$-module structure, where $R[G]$ is a group-ring.

Published on 15 Apr 2026 - 6:37

score 91 · Answer 12 · 2026-03-26 19:01:51

91

Views

A module $J$ is injective iff every short exact sequence of the form $0\to J\to A\to B\to 0$ splits.

Published on 26 Mar 2026 - 19:01

score 73 · Answer 13 · 2026-04-16 13:07:15

73

Views

Assumptions for $\text{Ker}(p)=\text{Im}(i)$ to hold so that $0\xrightarrow{}N\xrightarrow{i}M\xrightarrow{p}P\xrightarrow{}0$ is exact?

Published on 16 Apr 2026 - 13:07

score 96 · Answer 14 · 2026-04-14 22:15:21

96

Views

$\mathrm{Hom}_A(\prod_i M_i, N) \cong \prod_i \mathrm{Hom}_A(M_i, N)$ and $\mathrm{Hom}_A (M, \bigoplus_i N_i) \cong \prod_i \mathrm{Hom}_A(M, N_i)$?

Published on 14 Apr 2026 - 22:15

score 25 · Answer 15 · 2026-04-10 13:48:38

25

Views

Surjectivity of $A^G/NA\to H^2(G,A)$ for $G$ finite cyclic

Published on 10 Apr 2026 - 13:48

List Question

Are these approaches for proving that a function is well-defined the same?

$R$-algebras and the tensor-algebra.

Is this Proof of Well-definedness Correct?

Is the inverse of a finitely generated $A$-submodule of $\mathrm{Frac}(A)$ still finitely generated?

Show that the statements about module $M_R$ are equivalent.

Must I Prove Exactness at these Points as Well?

tensor product of modules over tensor product

cyclic $R$-module correspondence in $R$ which is PID

Proof of $\operatorname{rank}(M) = \operatorname{rank}(M/\operatorname{Tor}(M))$

Unique $R$-algebra homomorphism from the exterior algebra to an $R$-algebra $A$, if $a^2 = 0$ for all $a \in A$.

Is there a way to determine when an abelian group $(M,+)$ admits a $R[G]$-module structure, where $R[G]$ is a group-ring.

A module $J$ is injective iff every short exact sequence of the form $0\to J\to A\to B\to 0$ splits.

Assumptions for $\text{Ker}(p)=\text{Im}(i)$ to hold so that $0\xrightarrow{}N\xrightarrow{i}M\xrightarrow{p}P\xrightarrow{}0$ is exact?

$\mathrm{Hom}_A(\prod_i M_i, N) \cong \prod_i \mathrm{Hom}_A(M_i, N)$ and $\mathrm{Hom}_A (M, \bigoplus_i N_i) \cong \prod_i \mathrm{Hom}_A(M, N_i)$?

Surjectivity of $A^G/NA\to H^2(G,A)$ for $G$ finite cyclic

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