# Ring detail

## Name: Bass's right-not-left perfect ring

Description: Let $S$ be the subset of infinite matrices over a countably infinite field $k$ which are nonzero only on finitely many entries above the diagonal. $R$ is the subring of the matrix ring generated by $S$ and the "infinite" identity matrix.

Keywords infinite matrix ring subring

Reference(s):

• T.-Y. Lam. A first course in noncommutative rings. (2013) @ pp 345-346

Legend
• = has the property
• = does not have the property
• = information not in database
Name Measure
cardinality $\aleph_0$
composition length left: $\infty$right: $\infty$
Name Description
Idempotents $\{0,1\}$