List questions from ring-theory

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Interesting pairs of properties and relations in ring theory

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Ring without zero divisor (Proof)

Published on 03 Nov 2018 - 11:34

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How can I prove that any field of order $p^n$ has a unique subring of order $p^m$ where $m$ divides $n$.

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Notations concerning polynomials over and extensions of rings

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$S_m(F)=\{a\in F:a^{p^m}=a\}$. $S_m (F)$ is a subfield of the field $F$.

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Showing that $\mathbb Z[i]/(p)\simeq \mathbb Z[i]/(\pi)\times\mathbb Z[i]/(\overline\pi )$

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Additive group of tensor product of commutative $k$-algebras with units

Published on 03 Nov 2018 - 20:16

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Let $R$ be an integral domain. If $x \in R$ is prime, then $x$ is irreducible.

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Unitary Ring of Endomorphisms.

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Is the polynomial $x^2+1$ reducible in $\mathbb Z_7[x]$?

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Artin-Rees property in commutative Noetherian rings with unit

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What units are in the ring $\mathbb{Z}_2 \times \mathbb{Z}$?

Published on 05 Nov 2018 - 10:33

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Do zero divisor pairs in reduced rings always come from two distinct minimal prime ideals?

Published on 05 Nov 2018 - 13:21

201

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A Semiring without distributive property

Published on 27 Mar 2026 - 12:21

List Question

Prove for every $i∈\Bbb Z∪{0}$ that $N(b^i)<N(b^{i+1})$ .

Interesting pairs of properties and relations in ring theory

Ring without zero divisor (Proof)

How can I prove that any field of order $p^n$ has a unique subring of order $p^m$ where $m$ divides $n$.

Notations concerning polynomials over and extensions of rings

$S_m(F)=\{a\in F:a^{p^m}=a\}$. $S_m (F)$ is a subfield of the field $F$.

Showing that $\mathbb Z[i]/(p)\simeq \mathbb Z[i]/(\pi)\times\mathbb Z[i]/(\overline\pi )$

Additive group of tensor product of commutative $k$-algebras with units

Let $R$ be an integral domain. If $x \in R$ is prime, then $x$ is irreducible.

Unitary Ring of Endomorphisms.

Is the polynomial $x^2+1$ reducible in $\mathbb Z_7[x]$?

Artin-Rees property in commutative Noetherian rings with unit

What units are in the ring $\mathbb{Z}_2 \times \mathbb{Z}$?

Do zero divisor pairs in reduced rings always come from two distinct minimal prime ideals?

A Semiring without distributive property

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