Question

Residue field of a local ring as field extension

score 1.3k · Answer 1 · 2026-04-13 06:41:39

1.3k

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Residue field of a local ring as field extension

Published on 13 Apr 2026 - 6:41

score 3k · Answer 2 · 2026-04-15 06:15:46

3k

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If $k>0$ is a positive integer and $p$ is any prime, when is $\mathbb Z_p[\sqrt{k}] =\{a + b\sqrt k~|~a,b \in\mathbb Z_p\}$ a field.

Published on 15 Apr 2026 - 6:15

score 149 · Answer 3 · 2026-04-10 16:25:02

149

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Finding a particular principal open subset of $Spec R$

Published on 10 Apr 2026 - 16:25

score 60 · Answer 4 · 2026-04-17 13:36:55

60

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Ordered rings $R$ with $ab = ba$, $ab \leq ba$ or $ba \leq ab$ for all $a, b \in R$?

Published on 17 Apr 2026 - 13:36

score 190 · Answer 5 · 2026-04-15 04:17:00

190

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One dimensional noetherian domain

Published on 15 Apr 2026 - 4:17

score 1.2k · Answer 6 · 2026-04-24 03:54:28

1.2k

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What is an example of two k-algebras that are isomorphic as rings, but not as k-algebras?

Published on 24 Apr 2026 - 3:54

score 98 · Answer 7 · 2026-04-14 10:05:15

98

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Kernels of power surjective maps

Published on 14 Apr 2026 - 10:05

score 27.1k · Answer 8 · 2026-04-09 12:42:19

27.1k

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What is Abstract Algebra essentially?

Published on 09 Apr 2026 - 12:42

score 3.5k · Answer 9 · 2026-04-16 09:56:09

3.5k

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Suppose that $R$ is a commutative ring with no zero divisors. Show that all non zero elements of $R$ have the same additive order.

Published on 16 Apr 2026 - 9:56

score 462 · Answer 10 · 2026-04-13 03:36:20

462

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Ring Structures On $\mathbb {R} ^n$

Published on 13 Apr 2026 - 3:36

score 625 · Answer 11 · 2026-04-15 07:15:35

625

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Role of Commutative Ring? Suppose that $R$ is a commutative ring with no zero divisors, then Char $R$ is $0$ or prime.

Published on 15 Apr 2026 - 7:15

score 542 · Answer 12 · 2026-04-10 10:31:50

542

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Is the completion of a Dedekind domain a PID?

Published on 10 Apr 2026 - 10:31

score 137 · Answer 13 · 2026-04-15 05:37:23

137

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(True/False)? If $R$ is a commutative ring, then prove that $(s \cdot t) x =(s \cdot x)(t \cdot x) ; x \in R~,~s,t \in Z$

Published on 15 Apr 2026 - 5:37

score 102 · Answer 14 · 2026-04-24 05:17:36

102

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A question related to associated prime ideals

Published on 24 Apr 2026 - 5:17

score 952 · Answer 15 · 2026-04-16 10:43:42

952

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Any finite ring is a direct sum of rings of prime power order

Published on 16 Apr 2026 - 10:43

List Question

Residue field of a local ring as field extension

If $k>0$ is a positive integer and $p$ is any prime, when is $\mathbb Z_p[\sqrt{k}] =\{a + b\sqrt k~|~a,b \in\mathbb Z_p\}$ a field.

Finding a particular principal open subset of $Spec R$

Ordered rings $R$ with $ab = ba$, $ab \leq ba$ or $ba \leq ab$ for all $a, b \in R$?

One dimensional noetherian domain

What is an example of two k-algebras that are isomorphic as rings, but not as k-algebras?

Kernels of power surjective maps

What is Abstract Algebra essentially?

Suppose that $R$ is a commutative ring with no zero divisors. Show that all non zero elements of $R$ have the same additive order.

Ring Structures On $\mathbb {R} ^n$

Role of Commutative Ring? Suppose that $R$ is a commutative ring with no zero divisors, then Char $R$ is $0$ or prime.

Is the completion of a Dedekind domain a PID?

(True/False)? If $R$ is a commutative ring, then prove that $(s \cdot t) x =(s \cdot x)(t \cdot x) ; x \in R~,~s,t \in Z$

A question related to associated prime ideals

Any finite ring is a direct sum of rings of prime power order

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