Ring $R_{ 21 }$

Left-not-right Noetherian domain


Twisted polynomials $k[x;\sigma]$ for a countable division ring $k$ with endomorphism $\sigma$ which isn't an automorphism. The twist is given by $xa=\sigma(a)x$.

Keywords twisted (skew) polynomial ring


  • T.-Y. Lam. A first course in noncommutative rings. (2013) @ p 21

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