# Ring detail

## Name: $k[x;\sigma]/(x^2)$ (not right Artinian)

Description: Let $\sigma:k\to k$ be a field endomorphism of a countable field $k$ such that $\infty =[k:\sigma(k)]>1$. $k[x;\sigma]$ is the twisted polynomial ring where $xa:=\sigma(a)x$ for all $a$ in $k$. The ring is $k[x;\sigma]/(x^2)$.

Keywords quotient ring twisted (skew) ring

Reference(s):

• E. A. Rutter and Jr. Rings with the principal extension property. (1975) @ Example 1, pp 208-209

Legend
• = has the property
• = does not have the property
• = information not in database

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