Ring $R_{ 44 }$

Bass's right-not-left perfect ring


Let $S$ be the subset of infinite matrices over $\mathbb Q$ 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


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

  • = has the property
  • = does not have the property
  • = information not in database
Name Measure
cardinality $\aleph_0$
composition length left: $\infty$right: $\infty$
Krull dimension (classical) 0
Name Description
Idempotents $\{0,1\}$
Jacobson radical $S$
Left socle Elements of $S$ that are nonzero only on the top row.
Nilpotents $S$
prime radical $S$
Right socle $\{0\}$
Unique maximal ideal $S$
Units $R\setminus S$
Zero divisors $S$