List questions from ring-theory

Published on 26 Mar 2026 - 4:29

56

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Non fundamental point with local ring integrally closed is necessarily regular?

Published on 14 Apr 2026 - 3:01

119

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How to prove that if $x$ is not invertible, then $Rx \neq R$?

Published on 12 Apr 2026 - 20:46

598

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Division of Eisenstein Integers

Published on 28 Apr 2026 - 13:48

228

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Another proof of $\phi (p^r) = (p-1)p^{r-1}$

Published on 14 Apr 2026 - 4:30

31

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Proving that if $m \in \mathbb{Z}$, then $\left]m,m+1\right[ = \emptyset$ in $\mathbb{Z}$.

Published on 15 Apr 2026 - 23:41

71

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The product of non-unital rings

Published on 11 Apr 2026 - 0:45

98

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Given prime ideal $P$ of ring $R$, does $RrR\subset P$ imply $r\in P$ for $r\in R$? (Hungerford)

Published on 10 May 2026 - 17:02

146

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Product of ideals in non-commutative, non-unital ring

Published on 13 Apr 2026 - 3:10

244

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Prove that $I$ is a finitely-generated ideal of $\mathbb{Z}[x]$ by finding a finite set of generators for $I$.

Published on 09 Apr 2026 - 21:02

184

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$\begin{pmatrix} a & b \\ 0 & c \end{pmatrix}$ has an inverse $\implies a,c$ have inverses?

Published on 17 Apr 2026 - 6:05

131

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List the distinct principal ideals in $\mathbb{ℤ}_5 \times \mathbb{ℤ}_{12}$

Published on 13 Apr 2026 - 0:51

665

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Jacobson Radical of semisimple module

Published on 09 Apr 2026 - 10:08

202

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Idempotents in $\Bbb Z_2[x]/(x^7+1)$

Published on 26 Mar 2026 - 4:16

220

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Quotient ring is Prime iff the ideal is prime ideal

Published on 13 Apr 2026 - 0:42

List Question

Does being principal ideal ring with identity implies PID?

Non fundamental point with local ring integrally closed is necessarily regular?

How to prove that if $x$ is not invertible, then $Rx \neq R$?

Division of Eisenstein Integers

Another proof of $\phi (p^r) = (p-1)p^{r-1}$

Proving that if $m \in \mathbb{Z}$, then $\left]m,m+1\right[ = \emptyset$ in $\mathbb{Z}$.

The product of non-unital rings

Given prime ideal $P$ of ring $R$, does $RrR\subset P$ imply $r\in P$ for $r\in R$? (Hungerford)

Product of ideals in non-commutative, non-unital ring

Prove that $I$ is a finitely-generated ideal of $\mathbb{Z}[x]$ by finding a finite set of generators for $I$.

$\begin{pmatrix} a & b \\ 0 & c \end{pmatrix}$ has an inverse $\implies a,c$ have inverses?

List the distinct principal ideals in $\mathbb{ℤ}_5 \times \mathbb{ℤ}_{12}$

Jacobson Radical of semisimple module

Idempotents in $\Bbb Z_2[x]/(x^7+1)$

Quotient ring is Prime iff the ideal is prime ideal

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