List questions from artinian | MathQa

Nilpotent or just nil idempotent ideal?

Published on 12 Jan 2025 - 21:11

Example of a non noetherian module $M$ s.t. $M/IM$ is noetherian

Published on 12 Jan 2025 - 21:28

Let $R$ be a ring and $I$ be a finitely generated nilpotent ideal. If $R/I$ is noetherian (resp. Artinian) then $R$ is so.

Published on 12 Jan 2025 - 21:43

Proof of commutative Artinian ring is Noetherian

Published on 12 Jan 2025 - 21:19

Can we find ( characterize ) all non-zero commutative Artinian rings $R$ for which $-1 , 1$ are the only units of $R$ ?

Published on 12 Jan 2025 - 21:42

Artinian - Noetherian rings and modules suggest study guide

Published on 12 Jan 2025 - 21:26

Dimension of an Artin $K$-algebra and cardinal of its spectrum

Published on 12 Jan 2025 - 21:27

If $R/I$ and $R/J$ are Noetherian (resp. Artinian), then so is $R/(I \cap J)$

Published on 12 Jan 2025 - 21:31

$M$ is a $\Bbb Z/36 \Bbb Z$-module and $\bar 6 \cdot M = \{0\}$. Prove: $M$ is Noetherian $\iff$ it's Artinian

Published on 12 Jan 2025 - 21:38

Quotient of free algebra - Noetherian/Artinian?

Published on 12 Jan 2025 - 21:16