Question

Confusion with quotient module of cyclic groups

score 19 · Answer 1 · 2019-06-16 23:33:57

19

Views

Confusion with quotient module of cyclic groups

Published on 16 Jun 2019 - 23:33

score 170 · Answer 2 · 2026-04-02 15:11:15

170

Views

Space of Homomorphisms Between Two Group Modules

Published on 02 Apr 2026 - 15:11

score 31 · Answer 3 · 2019-06-17 17:37:17

31

Views

All elements of $N := \oplus_{p \in \mathcal{P}} \mathbb{Z}/p\mathbb{Z}$ are of finite order

Published on 17 Jun 2019 - 17:37

score 283 · Answer 4 · 2019-06-17 19:33:45

283

Views

Finite rank implies finitely generated?

Published on 17 Jun 2019 - 19:33

score 46 · Answer 5 · 2019-06-17 21:42:11

if $A$ is compact $\Bbb{Z}_p$ - module such that $A/pA$ is finite, then $A$ is finitely generated over $\Bbb{Z}_p$.

score 319 · Answer 6 · 2019-06-18 18:31:20

319

Views

What does 'every monomorphism in $R$-$\mathsf{Mod}$ is a kernel' mean?

Published on 18 Jun 2019 - 18:31

score 351 · Answer 7 · 2019-06-18 23:49:07

351

Views

Prove that there is a natural bijection between the set of $R[x]$-module structures on $M$ and $\mathrm{End}_{R-\mathsf{Mod}}(M)$.

Published on 18 Jun 2019 - 23:49

score 147 · Answer 8 · 2019-06-19 17:01:21

147

Views

Commutative Diagrams in R-algebra

Published on 19 Jun 2019 - 17:01

score 53 · Answer 9 · 2019-06-19 17:11:34

53

Views

If $R$ is commutative and $M$ is an $R$-module, does every element of $R$ determine an $R$-module endomorphism of $M$?

Published on 19 Jun 2019 - 17:11

score 81 · Answer 10 · 2019-06-19 21:04:14

81

Views

Why is $\varphi: R[A] \to S$ automatically an $R$-module homomorphism?

Published on 19 Jun 2019 - 21:04

score 33 · Answer 11 · 2026-03-28 01:12:44

33

Views

Give an estimate for the approximation $a^n=b^n$

Published on 28 Mar 2026 - 1:12

score 144 · Answer 12 · 2019-06-20 20:55:45

144

Views

$\mathbb{Z}/m\mathbb{Z} \otimes_{\mathbb{Z}}\mathbb{Z}/n\mathbb{Z} \cong \mathbb{Z}/d\mathbb{Z}$

Published on 20 Jun 2019 - 20:55

score 19 · Answer 13 · 2026-03-25 04:36:09

19

Views

Going back and forth between algebra $A$ and regular module ${}_AA$ in GAP

Published on 25 Mar 2026 - 4:36

score 568 · Answer 14 · 2019-06-22 02:17:53

568

Views

$\varphi: M \to N$ is onto if and only if for all $R$-mod homomorphisms $\alpha : F \to N$ there exists an $R$-mod homomorphism $\beta : F \to M$

Published on 22 Jun 2019 - 2:17

score 134 · Answer 15 · 2019-06-22 04:47:13

134

Views

Let $N$ be an $R$-module. Prove $\mathrm{Hom}_{R-\mathsf{Mod}}(R/I, N) \cong \{n \in N \mid \forall a \in I, an=0\}$.

Published on 22 Jun 2019 - 4:47

List Question

Confusion with quotient module of cyclic groups

Space of Homomorphisms Between Two Group Modules

All elements of $N := \oplus_{p \in \mathcal{P}} \mathbb{Z}/p\mathbb{Z}$ are of finite order

Finite rank implies finitely generated?

if $A$ is compact $\Bbb{Z}_p$ - module such that $A/pA$ is finite, then $A$ is finitely generated over $\Bbb{Z}_p$.

What does 'every monomorphism in $R$-$\mathsf{Mod}$ is a kernel' mean?

Prove that there is a natural bijection between the set of $R[x]$-module structures on $M$ and $\mathrm{End}_{R-\mathsf{Mod}}(M)$.

Commutative Diagrams in R-algebra

If $R$ is commutative and $M$ is an $R$-module, does every element of $R$ determine an $R$-module endomorphism of $M$?

Why is $\varphi: R[A] \to S$ automatically an $R$-module homomorphism?

Give an estimate for the approximation $a^n=b^n$

$\mathbb{Z}/m\mathbb{Z} \otimes_{\mathbb{Z}}\mathbb{Z}/n\mathbb{Z} \cong \mathbb{Z}/d\mathbb{Z}$

Going back and forth between algebra $A$ and regular module ${}_AA$ in GAP

$\varphi: M \to N$ is onto if and only if for all $R$-mod homomorphisms $\alpha : F \to N$ there exists an $R$-mod homomorphism $\beta : F \to M$

Let $N$ be an $R$-module. Prove $\mathrm{Hom}_{R-\mathsf{Mod}}(R/I, N) \cong \{n \in N \mid \forall a \in I, an=0\}$.

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