Ring $R_{ 109 }$

Cozzens' simple V-domain


Let $F$ be the algebraic closure of the field of two elements, and $F[t, \sigma]$ be the twisted polynomial ring with $\sigma$ is the automorphism $x\mapsto x^2$ on $F$. Finally, $R$ is the localization $F[t,\sigma]S^{-1}$ where $S$ is the set of nonnegative powers of $t$.

Notes: Has a unique simple right $R$ module (up to isomorphism)

Keywords localization twisted (skew) polynomial ring


  • J. H. Cozzens. Homological properties of the ring of differential polynomials. (1970) @ Section 2

  • = has the property
  • = does not have the property
  • = information not in database
Name Measure
cardinality $\aleph_0$
global dimension left: 1right: 1
Name Description
Idempotents $\{0,1\}$
Jacobson radical $\{0\}$
Left singular ideal $\{0\}$
Left socle $\{0\}$
Nilpotents $\{0\}$
Right singular ideal $\{0\}$
Right socle $\{0\}$
Zero divisors $\{0\}$