Question

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

score 54 · Answer 1 · 2026-04-02 23:23:25

54

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 02 Apr 2026 - 23:23

score 82 · Answer 2 · 2026-04-02 23:25:07

82

Views

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

Published on 02 Apr 2026 - 23:25

score 234 · Answer 3 · 2019-06-20 04:36:33

234

Views

Is the direct product of Euclidean rings (not necessarily integral domains) also Euclidean?

Published on 20 Jun 2019 - 4:36

score 149 · Answer 4 · 2026-03-26 10:04:41

149

Views

Minimal primary decomposition of ideal in $k[x,y,z]$

Published on 26 Mar 2026 - 10:04

score 154 · Answer 5 · 2026-03-29 15:33:02

154

Views

Short Question: $(p)$ for a prime is not a maximal ideal in $\mathbb{Z}[X]$

Published on 29 Mar 2026 - 15:33

score 120 · Answer 6 · 2026-04-08 06:37:26

120

Views

Relationship between Cyclic group and Field

Published on 08 Apr 2026 - 6:37

score 133 · Answer 7 · 2019-06-21 02:53:40

133

Views

Reducing Congruences modulo an ideal of a ring of algebraic integers to congruences over $\mathbb{Z}$

Published on 21 Jun 2019 - 2:53

score 73 · Answer 8 · 2019-06-21 13:37:17

73

Views

Show the following is a subring of $\mathbb{C}$

Published on 21 Jun 2019 - 13:37

score 655 · Answer 9 · 2026-03-29 15:40:30

655

Views

On the maximal ideals of $\Bbb Z_5[X,Y]$ which contain $\langle Y \rangle$

Published on 29 Mar 2026 - 15:40

score 42 · Answer 10 · 2026-03-28 01:46:14

42

Views

Isomorphism from $(\mathbb{Z}/200\mathbb{Z})^\times$

Published on 28 Mar 2026 - 1:46

score 569 · Answer 11 · 2026-04-02 23:22:08

569

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 02 Apr 2026 - 23:22

score 135 · Answer 12 · 2026-04-02 23:21:49

135

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 02 Apr 2026 - 23:21

score 161 · Answer 13 · 2019-06-22 13:35:53

161

Views

$\operatorname{Spec} k[x_1,...,x_n]/(f(x_1,...,x_n))$ for$ f(x_1,...,x_n)$ irreducible are all homeomorphic?

Published on 22 Jun 2019 - 13:35

score 377 · Answer 14 · 2019-06-22 15:32:57

377

Views

Question about Proof of Eisenstein's Criterion for integral domains

Published on 22 Jun 2019 - 15:32

score 25 · Answer 15 · 2019-06-22 16:22:14

25

Views

$Z(D) \cong Z(\text{Mat}_n(D))$

Published on 22 Jun 2019 - 16:22

List Question

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?

Is the direct product of Euclidean rings (not necessarily integral domains) also Euclidean?

Minimal primary decomposition of ideal in $k[x,y,z]$

Short Question: $(p)$ for a prime is not a maximal ideal in $\mathbb{Z}[X]$

Relationship between Cyclic group and Field

Reducing Congruences modulo an ideal of a ring of algebraic integers to congruences over $\mathbb{Z}$

Show the following is a subring of $\mathbb{C}$

On the maximal ideals of $\Bbb Z_5[X,Y]$ which contain $\langle Y \rangle$

Isomorphism from $(\mathbb{Z}/200\mathbb{Z})^\times$

$\varphi: M \to N$ 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 $\mathrm{Hom}_{R-\mathsf{Mod}}(R/I, N) \cong \{n \in N \mid \forall a \in I, an=0\}$.

$\operatorname{Spec} k[x_1,...,x_n]/(f(x_1,...,x_n))$ for$ f(x_1,...,x_n)$ irreducible are all homeomorphic?

Question about Proof of Eisenstein's Criterion for integral domains

$Z(D) \cong Z(\text{Mat}_n(D))$

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