List questions from ring-theory

Published on 28 Mar 2026 - 8:19

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Statement about semisimple quotient ring.

Published on 12 Nov 2018 - 16:34

241

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Suppose that $R$ is a commutative ring, $P$ is a prime ideal, and $P\subseteq \langle a\rangle$,where $a\notin P$. Show $P=aP=\{ax:x\in P\}$

Published on 12 Nov 2018 - 21:12

2.3k

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Let $R$ be a finite commutative ring with unity. Show that every prime ideal of $R$ is maximal.

Published on 12 Nov 2018 - 22:04

216

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Rings and categories with zero Grothendieck group

Published on 24 Mar 2026 - 22:09

165

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Is it true that summation of ideals equal to ideal generated by their generator

Published on 13 Nov 2018 - 2:08

41

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nonuniform local ring with essential socle

Published on 30 Mar 2026 - 0:03

1.4k

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Why $K[[X]]$ is PID and what's the form of the ring's ideals?

Published on 25 Mar 2026 - 18:57

57

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Injective endomorphism and determinant

Published on 14 Nov 2018 - 1:30

251

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How to show the canonical homomorphism $A_{\mathfrak p}\to B_{\mathfrak q}$ is injective?

Published on 14 Nov 2018 - 5:13

46

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Do we have $\ker (f)_{\mathfrak p}\simeq \ker (g)$?

Published on 14 Nov 2018 - 6:37

1.4k

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Prime ideals and integral domains

Published on 29 Mar 2026 - 18:13

142

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Prove that $Y^n-13X^4$ is irreducible in $\mathbf{Q}[X,Y]$

Published on 14 Nov 2018 - 13:53

91

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Writing out a maximal sub-field of $R$

Published on 14 Nov 2018 - 13:59

265

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Constructing a local non-Noetherian domain with spectrum $\{(0), \mathfrak{m} \}$.

Published on 15 Nov 2018 - 0:21

List Question

Fundamental homomorphism theorem (epimorphism)

Statement about semisimple quotient ring.

Suppose that $R$ is a commutative ring, $P$ is a prime ideal, and $P\subseteq \langle a\rangle$,where $a\notin P$. Show $P=aP=\{ax:x\in P\}$

Let $R$ be a finite commutative ring with unity. Show that every prime ideal of $R$ is maximal.

Rings and categories with zero Grothendieck group

Is it true that summation of ideals equal to ideal generated by their generator

nonuniform local ring with essential socle

Why $K[[X]]$ is PID and what's the form of the ring's ideals?

Injective endomorphism and determinant

How to show the canonical homomorphism $A_{\mathfrak p}\to B_{\mathfrak q}$ is injective?

Do we have $\ker (f)_{\mathfrak p}\simeq \ker (g)$?

Prime ideals and integral domains

Prove that $Y^n-13X^4$ is irreducible in $\mathbf{Q}[X,Y]$

Writing out a maximal sub-field of $R$

Constructing a local non-Noetherian domain with spectrum $\{(0), \mathfrak{m} \}$.

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