Question

$\mathbb{Z}^m\hookrightarrow\mathbb{Z}^n$ implies $m\le n$

score 71 · Answer 1 · 2026-04-11 17:05:56

71

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$\mathbb{Z}^m\hookrightarrow\mathbb{Z}^n$ implies $m\le n$

Published on 11 Apr 2026 - 17:05

score 62 · Answer 2 · 2026-04-07 18:55:39

62

Views

Properties of finite group and their subgroup.

Published on 07 Apr 2026 - 18:55

score 46 · Answer 3 · 2026-04-10 09:27:18

46

Views

Prime ideals in ring and polynomial rings

Published on 10 Apr 2026 - 9:27

score 436 · Answer 4 · 2026-04-17 05:17:34

436

Views

Completion of Noetherian ring $A$ by $I=(a_1,\ldots,a_n)$ is isomorphic to $A[[x_1,\ldots,x_n]]/(x_1-a_1,\ldots,x_n-a_n)$

Published on 17 Apr 2026 - 5:17

score 99 · Answer 5 · 2026-04-17 02:13:28

99

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Why do we specify the degree of elements in algebra?

Published on 17 Apr 2026 - 2:13

score 1.6k · Answer 6 · 2026-04-16 22:27:07

1.6k

Views

A non-zero ring $R$ is a field if and only if for any non-zero ring $S$, any ring homomorphism from $R$ to $S$ is injective.

Published on 16 Apr 2026 - 22:27

score 55 · Answer 7 · 2026-04-29 12:49:43

55

Views

Is that specific function additive under disjoint union?

Published on 29 Apr 2026 - 12:49

score 51 · Answer 8 · 2026-04-13 05:09:12

51

Views

Prove $\langle k \rangle \big/ \langle n\rangle$ is isomorphic to $\mathbb{Z}_{(n/k)}$.

Published on 13 Apr 2026 - 5:09

score 1.1k · Answer 9 · 2026-04-16 16:58:58

1.1k

Views

Let $G$ be a group of order $8$ and $x$ be an element of $G$ of order $4$. Prove that $x^2 \in Z(G)$

Published on 16 Apr 2026 - 16:58

score 82 · Answer 10 · 2026-04-16 00:47:41

82

Views

Computing the number of elements in a finite field $F$

Published on 16 Apr 2026 - 0:47

score 73 · Answer 11 · 2026-04-14 06:51:56

73

Views

Prove for any nonzero polynomial $f\in \mathbb{Z}_p$ these statements are equivalent

Published on 14 Apr 2026 - 6:51

score 613 · Answer 12 · 2026-04-11 07:01:35

613

Views

What is an ideal generated by a polynomial in $\mathbb{Z}_n[x]$ and what is $\mathbb{Z}_n[x]/<p(x)>$?

Published on 11 Apr 2026 - 7:01

score 222 · Answer 13 · 2026-04-16 13:40:05

222

Views

Do there exist two non-isomorphic fields whose additive groups are isomorphic and whose multiplicative groups are isomorphic

Published on 16 Apr 2026 - 13:40

score 103 · Answer 14 · 2026-04-16 08:53:06

103

Views

Given is a 2x2 matrix. Deduce a necessary and sufficient condition that this matrix is regular

Published on 16 Apr 2026 - 8:53

score 2.8k · Answer 15 · 2026-04-11 06:56:53

2.8k

Views

How is an infinite direct sum defined?

Published on 11 Apr 2026 - 6:56

List Question

$\mathbb{Z}^m\hookrightarrow\mathbb{Z}^n$ implies $m\le n$

Properties of finite group and their subgroup.

Prime ideals in ring and polynomial rings

Completion of Noetherian ring $A$ by $I=(a_1,\ldots,a_n)$ is isomorphic to $A[[x_1,\ldots,x_n]]/(x_1-a_1,\ldots,x_n-a_n)$

Why do we specify the degree of elements in algebra?

A non-zero ring $R$ is a field if and only if for any non-zero ring $S$, any ring homomorphism from $R$ to $S$ is injective.

Is that specific function additive under disjoint union?

Prove $\langle k \rangle \big/ \langle n\rangle$ is isomorphic to $\mathbb{Z}_{(n/k)}$.

Let $G$ be a group of order $8$ and $x$ be an element of $G$ of order $4$. Prove that $x^2 \in Z(G)$

Computing the number of elements in a finite field $F$

Prove for any nonzero polynomial $f\in \mathbb{Z}_p$ these statements are equivalent

What is an ideal generated by a polynomial in $\mathbb{Z}_n[x]$ and what is $\mathbb{Z}_n[x]/<p(x)>$?

Do there exist two non-isomorphic fields whose additive groups are isomorphic and whose multiplicative groups are isomorphic

Given is a 2x2 matrix. Deduce a necessary and sufficient condition that this matrix is regular

How is an infinite direct sum defined?

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