Question

Does every infinite field contain the integers as a subring?

score 1k · Answer 1 · 2026-04-18 06:47:55

1k

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Does every infinite field contain the integers as a subring?

Published on 18 Apr 2026 - 6:47

score 283 · Answer 2 · 2026-04-16 07:34:29

283

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In a noncommutative ring, is there always a pair $x,y$ such that $xy-yx=1$?

Published on 16 Apr 2026 - 7:34

score 2.2k · Answer 3 · 2026-04-14 10:40:21

2.2k

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Prime ideals in non-commutative ring

Published on 14 Apr 2026 - 10:40

score 93 · Answer 4 · 2026-04-10 13:57:55

93

Views

(Updated): Finding the kernel of a ring morphism

Published on 10 Apr 2026 - 13:57

score 2.9k · Answer 5 · 2026-04-13 07:30:56

2.9k

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List the distinct principal ideals in $\mathbb{ℤ}_2 \times \mathbb{ℤ}_3$

Published on 13 Apr 2026 - 7:30

score 75 · Answer 6 · 2026-04-28 01:35:43

75

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Idempotents in $\mathbf{CRing}$

Published on 28 Apr 2026 - 1:35

score 83 · Answer 7 · 2026-04-15 18:21:02

83

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Let $I$ be a proper ideal of a ring $R$. Then $IR[\alpha_1, ... , \alpha_n]$ is a proper ideal of $R[\alpha_1, ... , \alpha_n]$

Published on 15 Apr 2026 - 18:21

score 238 · Answer 8 · 2026-04-16 08:03:44

238

Views

Show that $\deg(fg) = m+n$

Published on 16 Apr 2026 - 8:03

score 285 · Answer 9 · 2026-04-14 21:38:01

285

Views

In $\mathbb{Z}_q$ where $q$ is prime, show that $[a^q]=[a]$ for all $[a]\in \mathbb{Z}_q$

Published on 14 Apr 2026 - 21:38

score 48 · Answer 10 · 2026-04-12 08:19:54

48

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The fundamental unit in the ring of algebraic integers. 1

Published on 12 Apr 2026 - 8:19

score 88 · Answer 11 · 2026-04-14 16:52:44

88

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Ideals and product of ideals

Published on 14 Apr 2026 - 16:52

score 49 · Answer 12 · 2026-04-14 00:20:48

49

Views

In $\mathbb Z[x]$, show that the only common divisors of $2$ and $x$ are $1$ and $-1$.

Published on 14 Apr 2026 - 0:20

score 3k · Answer 13 · 2026-04-12 18:18:02

3k

Views

why $\mathbb Z[\sqrt 2] \ncong \mathbb Z[\sqrt 3]$?

Published on 12 Apr 2026 - 18:18

score 134 · Answer 14 · 2026-04-10 20:27:56

134

Views

Simple Maximal Ideal Question.

Published on 10 Apr 2026 - 20:27

score 162 · Answer 15 · 2026-04-28 03:09:13

162

Views

Simple question on tensoring by a quotient ring

Published on 28 Apr 2026 - 3:09

List Question

Does every infinite field contain the integers as a subring?

In a noncommutative ring, is there always a pair $x,y$ such that $xy-yx=1$?

Prime ideals in non-commutative ring

(Updated): Finding the kernel of a ring morphism

List the distinct principal ideals in $\mathbb{ℤ}_2 \times \mathbb{ℤ}_3$

Idempotents in $\mathbf{CRing}$

Let $I$ be a proper ideal of a ring $R$. Then $IR[\alpha_1, ... , \alpha_n]$ is a proper ideal of $R[\alpha_1, ... , \alpha_n]$

Show that $\deg(fg) = m+n$

In $\mathbb{Z}_q$ where $q$ is prime, show that $[a^q]=[a]$ for all $[a]\in \mathbb{Z}_q$

The fundamental unit in the ring of algebraic integers. 1

Ideals and product of ideals

In $\mathbb Z[x]$, show that the only common divisors of $2$ and $x$ are $1$ and $-1$.

why $\mathbb Z[\sqrt 2] \ncong \mathbb Z[\sqrt 3]$?

Simple Maximal Ideal Question.

Simple question on tensoring by a quotient ring

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