Ring $R_{ 110 }$

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


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) polynomial ring


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

  • = has the property
  • = does not have the property
  • = information not in database
Name Measure
Krull dimension (classical) 0
Name Description
Idempotents $\{0,1\}$