Matrix rings over ∗-regular rings and pseudo-rank functions

Pere Ara

Vol. 129 (1987), No. 2, 209–241

DOI: 10.2140/pjm.1987.129.209

Abstract

In this paper we obtain a characterization of those ∗-regular rings whose matrix rings are ∗-regular satisfying LPRP. This result allows us to obtain a structure theorem for the ∗-regular self-injective rings of type I which satisfy LPRP matricially.

Also, we are concerned with pseudo-rank functions and their corresponding metric completions. We show, amongst other things, that the LPRP axiom extends from a unit-regular ∗-regular ring to its completion with respect to a pseudo-rank function. Finally, we show that the property LPRP holds for some large classes of ∗-regular self-injective rings of type II.

Mathematical Subject Classification 2000

Primary: 16A28, 16A28

Secondary: 46K99, 16A42, 16A30

Milestones

Received: 3 June 1985

Published: 1 October 1987