List questions from ring-theory

Published on 11 Apr 2026 - 6:19

75

Views

A non-unital commutative ring with infinite elements such that each element $a$ satisfies $ab =0$ for infinitely many $b$'s

Published on 16 Apr 2026 - 11:49

2.1k

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Let $K$ be a field extension of $F$ and let $a \in K$. Show that $[F(a):F(a^3)] \leq 3$

Published on 14 Apr 2026 - 20:32

510

Views

Some residue field

Published on 24 Apr 2026 - 19:40

296

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Is there a more direct way of proving that this ring is an integral domain?

Published on 11 Apr 2026 - 19:27

801

Views

A nonregular local ring

Published on 15 Apr 2026 - 17:56

70

Views

Example of a ring which is not CM at all its prime ideals

Published on 11 Apr 2026 - 0:17

253

Views

Showing that $x^3+y^3+z^3=0$ is not rational

Published on 24 Apr 2026 - 21:19

703

Views

Characterizing Prime and Maximal Ideals in a nice Ring

Published on 15 Apr 2026 - 0:39

3.5k

Views

Sum and Product of two transcendental numbers cannot be simultaneously algebraic

Published on 10 Apr 2026 - 4:16

308

Views

Von Neumann regular but not self-injective ring

Published on 15 Apr 2026 - 9:51

291

Views

Characterizing maximal ideals in $\mathbb{Z}[x]$

Published on 11 Apr 2026 - 10:06

213

Views

The spectrum of a commutative ring with unity and its "topology"

Published on 24 Apr 2026 - 21:19

196

Views

A matrix lies in a subring isomorphic to $\mathbb{C}$

Published on 14 Apr 2026 - 15:06

2.7k

Views

In $\mathbb{Z}/(n)$, does $(a) = (b)$ imply that $a$ and $b$ are associates?

Published on 14 Apr 2026 - 19:25

List Question

A field extension of prime degree

A non-unital commutative ring with infinite elements such that each element $a$ satisfies $ab =0$ for infinitely many $b$'s

Let $K$ be a field extension of $F$ and let $a \in K$. Show that $[F(a):F(a^3)] \leq 3$

Some residue field

Is there a more direct way of proving that this ring is an integral domain?

A nonregular local ring

Example of a ring which is not CM at all its prime ideals

Showing that $x^3+y^3+z^3=0$ is not rational

Characterizing Prime and Maximal Ideals in a nice Ring

Sum and Product of two transcendental numbers cannot be simultaneously algebraic

Von Neumann regular but not self-injective ring

Characterizing maximal ideals in $\mathbb{Z}[x]$

The spectrum of a commutative ring with unity and its "topology"

A matrix lies in a subring isomorphic to $\mathbb{C}$

In $\mathbb{Z}/(n)$, does $(a) = (b)$ imply that $a$ and $b$ are associates?

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