List questions from ring-theory

Published on 31 Oct 2018 - 18:53

40

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Finding Factors of $x^4+x^3+x^2+x+1 \in \mathbb{Z}_5[x]$

Published on 26 Mar 2026 - 2:56

264

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Ring of order $p^2$ must be commutative.

Published on 31 Oct 2018 - 22:26

622

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Every subset of ideals of $R$ has maximal element $\implies$ Every ideal of $R$ is finitely generated, if $R$ is Noetherian.

Published on 25 Mar 2026 - 4:42

179

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Dimension of $\mathbb{C}$-algebra $\mathbb{C}[x,y]/(x^{3},xy,y^{2})$

Published on 01 Nov 2018 - 9:46

70

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Question about the dimension of elements in quotient ring

Published on 01 Nov 2018 - 10:20

375

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Ring expressed as union of ideals

Published on 01 Nov 2018 - 11:46

388

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Contraction of (non-prime) ideals in integral extensions

Published on 23 Feb 2026 - 2:29

31

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Prime elements in the ring of integers.

Published on 02 Apr 2026 - 3:46

403

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What are perfect squares in general rings?

Published on 25 Mar 2026 - 17:24

34

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Analogies and relations between evenness and squareness in arbitrary rings

Published on 25 Mar 2026 - 17:24

4k

Views

$(x,y)\subset \mathbb Q[x,y]$ is not a principal ideal

Published on 29 Mar 2026 - 16:20

53

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$n\mid d \iff a^d-1\mid a^n-1$ and prove field with $p^d$ elements is a subfield of a field with $p^n$ elements $\iff$ $d\mid n$

Published on 01 Nov 2018 - 23:19

1.4k

Views

Show that $eR\,\cap\,(1-e)R=\{0\}$ if $e$ is an idempotent in R

Published on 02 Nov 2018 - 6:05

98

Views

Bezout's identity on $F[x]$ with constraints

Published on 25 Mar 2026 - 13:59

List Question

$\mathbb{Z}_{(p)}/p\mathbb{Z}_{(p)} = \mathbb{F}_p.$

Finding Factors of $x^4+x^3+x^2+x+1 \in \mathbb{Z}_5[x]$

Ring of order $p^2$ must be commutative.

Every subset of ideals of $R$ has maximal element $\implies$ Every ideal of $R$ is finitely generated, if $R$ is Noetherian.

Dimension of $\mathbb{C}$-algebra $\mathbb{C}[x,y]/(x^{3},xy,y^{2})$

Question about the dimension of elements in quotient ring

Ring expressed as union of ideals

Contraction of (non-prime) ideals in integral extensions

Prime elements in the ring of integers.

What are perfect squares in general rings?

Analogies and relations between evenness and squareness in arbitrary rings

$(x,y)\subset \mathbb Q[x,y]$ is not a principal ideal

$n\mid d \iff a^d-1\mid a^n-1$ and prove field with $p^d$ elements is a subfield of a field with $p^n$ elements $\iff$ $d\mid n$

Show that $eR\,\cap\,(1-e)R=\{0\}$ if $e$ is an idempotent in R

Bezout's identity on $F[x]$ with constraints

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