# Ring detail

## Name: left-not-right simple socle ring

Description: Let $s:F\to F$ be a field automorphism such that $[F:s(F)]>1$. $F[x,s]$ is the skew polynomial ring where $xa:=s(a)x$ for all $a$ in $F$. The ring is $F[x;s]/(x^2)$.

Notes: Composition length different on both sides

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: