List questions from finite-rings

Published on 10 Feb 2018 - 4:58

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Galois Theory for Finite Local Commutative Rings

Published on 22 Feb 2026 - 22:53

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How do I find a ring with a primary ideal having n elements?

Published on 13 Jun 2018 - 19:25

130

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Subring of $\text{Mat}_n(Z_m)$ is commutative if $x^2=0 \implies x=0$.

Published on 01 Jul 2018 - 15:25

81

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What is the name of $(\mathbb{Z}_2^s, \oplus, \odot)$ and where is it studied?

Published on 11 Jul 2018 - 17:24

40

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if a ring is finite then the translation $x\rightarrow ax$ is surjective where $a\in A$ is regular

Published on 16 Sep 2018 - 16:11

662

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Factor $x^ 5 - x^4 - x^ 2 - 1$ modulo $16$, and over $\mathbb{Q }$

Published on 13 Oct 2018 - 17:49

97

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Show that $\Bbb Z_p[i]$ is isomorphic to $\Bbb Z_p[x]/\langle x^2+1\rangle$.

Published on 24 Oct 2018 - 9:38

130

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Let $R$ be a finitely generated subring of a number field. Is $R/I$ finite for every non-zero ideal of $R$?

Published on 28 Nov 2018 - 20:04

1.6k

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How to prove $\Bbb Z[i]/(1+2i)\cong \Bbb Z_5$?

Published on 03 Jan 2019 - 15:21

386

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How to solve systems of linear equations over a finite ring

Published on 11 Jan 2019 - 14:17

60

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Is $\frac{R[x]}{(f(x))}$ finite for $R$ finite and $f$ not monic polynomial?

Published on 18 Jan 2019 - 11:09

69

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The number of polynomial functions $f:A\to A$ is $|A|^2$ if and only if $x^2=x$ for all $x\in A$.

Published on 05 Mar 2019 - 14:25

262

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How to show that $2$ is invertible in a ring with odd cardinality?

Published on 06 Mar 2019 - 18:02

68

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Finding inverses in quotient rings

Published on 09 Mar 2019 - 11:32

List Question

Minimal ideal in commutative finite rings

Galois Theory for Finite Local Commutative Rings

How do I find a ring with a primary ideal having n elements?

Subring of $\text{Mat}_n(Z_m)$ is commutative if $x^2=0 \implies x=0$.

What is the name of $(\mathbb{Z}_2^s, \oplus, \odot)$ and where is it studied?

if a ring is finite then the translation $x\rightarrow ax$ is surjective where $a\in A$ is regular

Factor $x^ 5 - x^4 - x^ 2 - 1$ modulo $16$, and over $\mathbb{Q }$

Show that $\Bbb Z_p[i]$ is isomorphic to $\Bbb Z_p[x]/\langle x^2+1\rangle$.

Let $R$ be a finitely generated subring of a number field. Is $R/I$ finite for every non-zero ideal of $R$?

How to prove $\Bbb Z[i]/(1+2i)\cong \Bbb Z_5$?

How to solve systems of linear equations over a finite ring

Is $\frac{R[x]}{(f(x))}$ finite for $R$ finite and $f$ not monic polynomial?

The number of polynomial functions $f:A\to A$ is $|A|^2$ if and only if $x^2=x$ for all $x\in A$.

How to show that $2$ is invertible in a ring with odd cardinality?

Finding inverses in quotient rings

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