Question

Prove no zero divisors of a ring with a radical in $\mathbb{Z}_7$

score 292 · Answer 1 · 2026-04-14 14:34:18

292

Views

Prove no zero divisors of a ring with a radical in $\mathbb{Z}_7$

Published on 14 Apr 2026 - 14:34

score 434 · Answer 2 · 2026-05-11 00:47:04

434

Views

The only idempotent element in $\Bbb Z_{51}$ are $0$ and $1$.

Published on 11 May 2026 - 0:47

score 141 · Answer 3 · 2026-04-13 23:13:09

141

Views

Field of fractions of $O_L$ where $O_L$ is the integral closure of a integral domain $A$ in a field extension $L$

Published on 13 Apr 2026 - 23:13

score 135 · Answer 4 · 2026-04-17 00:49:15

135

Views

Suppose $ g$ has the property that if $f(x)≠0$, then $g(x)=0$. Then prove that $g(x)=0$ for all $x$.

Published on 17 Apr 2026 - 0:49

score 96 · Answer 5 · 2026-04-16 16:04:20

96

Views

Integral domains and representatives of associate classes

Published on 16 Apr 2026 - 16:04

score 184 · Answer 6 · 2026-04-14 23:30:03

184

Views

Prove that $g(x)=0$ for all $x$.

Published on 14 Apr 2026 - 23:30

score 115 · Answer 7 · 2026-04-10 16:16:53

115

Views

Abelian groups that arise as unit groups of discrete valuation rings

Published on 10 Apr 2026 - 16:16

score 359 · Answer 8 · 2026-04-11 05:12:56

359

Views

$2$ is irreducible in $\mathbb{Z}[\sqrt 5]$

Published on 11 Apr 2026 - 5:12

score 61 · Answer 9 · 2026-04-16 08:52:24

61

Views

When is $\left\{\begin{pmatrix} x & yb \\ y & x \\ \end{pmatrix} : x,y\in \mathbb{Q}\right\}$ an integral domain?

Published on 16 Apr 2026 - 8:52

score 3.7k · Answer 10 · 2026-04-16 22:27:10

3.7k

Views

A proof that $\mathbb{Z}_{p}$ is an integral domain if and only if $p$ is prime.

Published on 16 Apr 2026 - 22:27

score 98 · Answer 11 · 2026-04-15 20:44:05

98

Views

$S$ is a commutative integral domain and a finitely generated $R$-Module where $R$ is a subring of $S$. $R$ is a field iff $S$ is a field

Published on 15 Apr 2026 - 20:44

score 144 · Answer 12 · 2026-04-15 13:45:48

144

Views

Tensor product with any Noetherian integral domain is Noetherian

Published on 15 Apr 2026 - 13:45

score 352 · Answer 13 · 2026-05-11 01:34:50

352

Views

Unique factorization of an element in an UFD

Published on 11 May 2026 - 1:34

score 80 · Answer 14 · 2026-04-13 12:21:57

80

Views

GCD of {0} in integral domains

Published on 13 Apr 2026 - 12:21

score 173 · Answer 15 · 2026-04-13 04:36:47

173

Views

Why is infinite field so important here? Clearing my fundamental concept in ring theory.

Published on 13 Apr 2026 - 4:36

List Question

Prove no zero divisors of a ring with a radical in $\mathbb{Z}_7$

The only idempotent element in $\Bbb Z_{51}$ are $0$ and $1$.

Field of fractions of $O_L$ where $O_L$ is the integral closure of a integral domain $A$ in a field extension $L$

Suppose $ g$ has the property that if $f(x)≠0$, then $g(x)=0$. Then prove that $g(x)=0$ for all $x$.

Integral domains and representatives of associate classes

Prove that $g(x)=0$ for all $x$.

Abelian groups that arise as unit groups of discrete valuation rings

$2$ is irreducible in $\mathbb{Z}[\sqrt 5]$

When is $\left\{\begin{pmatrix} x & yb \\ y & x \\ \end{pmatrix} : x,y\in \mathbb{Q}\right\}$ an integral domain?

A proof that $\mathbb{Z}_{p}$ is an integral domain if and only if $p$ is prime.

$S$ is a commutative integral domain and a finitely generated $R$-Module where $R$ is a subring of $S$. $R$ is a field iff $S$ is a field

Tensor product with any Noetherian integral domain is Noetherian

Unique factorization of an element in an UFD

GCD of {0} in integral domains

Why is infinite field so important here? Clearing my fundamental concept in ring theory.

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