# Commutative ring detail

## Name: Kasch not semilocal ring

Description: Let $M$ be the direct sum of $\mathbb Z/p_i\mathbb Z$ where $p_i$ is the $i$'th prime. The ring $R$ is the trivial extension of $M$ by $\mathbb Z$: $\mathbb Z\times M$ with the multiplication operation $(n,a)(m,b):=(nm,nb+ma)$

Notes: Krull dimension $1$.

Keywords trivial extension

Reference(s):

• (Citation needed)

• This ring has the following properties:
The ring lacks the following properties:
We don't know if the ring has or lacks the following properties: