# Commutative ring detail

## Name: Perfect nonArtinian ring

Description: Let $F$ be a field, $V$ be an infinite dimensional $F$-vector space, and consider the trivial extension $F(+)V$.

Notes: Radical has square zero. Krull dimension $0$.

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: