Question

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

score 289 · Answer 1 · 2019-07-13 17:34:03

289

Views

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

Published on 13 Jul 2019 - 17:34

score 430 · Answer 2 · 2019-07-13 21:58:33

430

Views

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

Published on 13 Jul 2019 - 21:58

score 138 · Answer 3 · 2019-07-14 00:42:56

138

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 14 Jul 2019 - 0:42

score 132 · Answer 4 · 2019-07-19 14:58:35

132

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 19 Jul 2019 - 14:58

score 93 · Answer 5 · 2019-07-20 02:58:16

93

Views

Integral domains and representatives of associate classes

Published on 20 Jul 2019 - 2:58

score 182 · Answer 6 · 2019-07-20 17:51:48

182

Views

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

Published on 20 Jul 2019 - 17:51

score 112 · Answer 7 · 2019-08-07 21:00:32

112

Views

Abelian groups that arise as unit groups of discrete valuation rings

Published on 07 Aug 2019 - 21:00

score 357 · Answer 8 · 2019-08-11 15:55:18

357

Views

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

Published on 11 Aug 2019 - 15:55

score 58 · Answer 9 · 2019-08-17 07:10:16

58

Views

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

Published on 17 Aug 2019 - 7:10

score 3.7k · Answer 10 · 2019-08-18 18:16:01

3.7k

Views

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

Published on 18 Aug 2019 - 18:16

score 95 · Answer 11 · 2019-08-19 21:35:10

95

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 19 Aug 2019 - 21:35

score 141 · Answer 12 · 2019-08-22 18:19:13

141

Views

Tensor product with any Noetherian integral domain is Noetherian

Published on 22 Aug 2019 - 18:19

score 348 · Answer 13 · 2019-08-25 21:35:21

348

Views

Unique factorization of an element in an UFD

Published on 25 Aug 2019 - 21:35

score 77 · Answer 14 · 2019-08-26 15:03:45

77

Views

GCD of {0} in integral domains

Published on 26 Aug 2019 - 15:03

score 170 · Answer 15 · 2019-09-02 06:02:23

170

Views

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

Published on 02 Sep 2019 - 6:02

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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