List questions from ring-theory

Published on 14 Apr 2026 - 8:20

46

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Roots of a polynomial in an elementary subfield

Published on 15 Apr 2026 - 16:52

43

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abstract algebra field subring

Published on 28 Apr 2026 - 20:11

163

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Finite rings $R$ in which $x^{25}=x$ holds

Published on 14 Apr 2026 - 15:33

116

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False proof that $R_1[x]\cong R_2[x]$ implies $R_1\cong R_2$ (which is not true)

Published on 09 Apr 2026 - 22:25

199

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Proof: If $ϕ: R \to R'$ is a ring isomorphism, then its inverse $ϕ^{-1} : R' \to R$ is a ring homomorphism.

Published on 16 Apr 2026 - 17:09

878

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$\Bbb Z_n $ is an injective $\Bbb Z_n$-module

Published on 11 May 2026 - 9:30

1.4k

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Homomorphic image of principal ideal ring

Published on 13 Apr 2026 - 19:36

114

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Compute the order of $GL_d(\mathbb{Z}/p\mathbb{Z})$

Published on 10 Apr 2026 - 23:35

66

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Why general elements of ideal are non-zero divisors?

Published on 11 May 2026 - 0:43

127

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Possible Converse to a Corollary to the Artin-Wedderburn Theorem

Published on 12 Apr 2026 - 16:42

672

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Uniqueness of Artin-Wedderburn decomposition

Published on 16 Apr 2026 - 4:44

149

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Prove that $2$ and $2i$ are irreducible in $R = \{a+ 2b i \mid a,\,b\in \mathbb{Z}\}$

Published on 14 Apr 2026 - 15:22

41

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Eisenstein Criterion to verify a that a polynomial is irreducible

Published on 13 Apr 2026 - 7:57

230

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Proving that a map is an isomorphism

Published on 14 Apr 2026 - 22:04

List Question

Looking for a reference about a lemma about an augmentation ideal in a group ring

Roots of a polynomial in an elementary subfield

abstract algebra field subring

Finite rings $R$ in which $x^{25}=x$ holds

False proof that $R_1[x]\cong R_2[x]$ implies $R_1\cong R_2$ (which is not true)

Proof: If $ϕ: R \to R'$ is a ring isomorphism, then its inverse $ϕ^{-1} : R' \to R$ is a ring homomorphism.

$\Bbb Z_n $ is an injective $\Bbb Z_n$-module

Homomorphic image of principal ideal ring

Compute the order of $GL_d(\mathbb{Z}/p\mathbb{Z})$

Why general elements of ideal are non-zero divisors?

Possible Converse to a Corollary to the Artin-Wedderburn Theorem

Uniqueness of Artin-Wedderburn decomposition

Prove that $2$ and $2i$ are irreducible in $R = \{a+ 2b i \mid a,\,b\in \mathbb{Z}\}$

Eisenstein Criterion to verify a that a polynomial is irreducible

Proving that a map is an isomorphism

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