# Ring detail

## Name: Left-not-right Noetherian domain

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

Keywords twisted (skew) ring

Reference(s):

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

Legend
• = 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 $\{0,1\}$
Nilpotents $\{0\}$
Zero divisors $\{0\}$