# Ring detail

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

Description: Let $s:F\to F$ be a field endomorphism such that $[F:s(F)]>1$. $F[x,s]$ is the twisted 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

Krull dimension: 0

Reference(s):

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