Centers of regular self-injective rings

Kenneth R. Goodearl

Vol. 76 (1978), No. 2, 381–395

DOI: 10.2140/pjm.1978.76.381

Abstract

This paper is concerned with calculating centers of regular self-injective rings, particularly those obtained by completions with respect to rank functions, and those obtained as factor rings of other regular self-injective rings. Sufficient conditions are developed under which the completion of a regular ring R has the same center as R. For any regular self-injective ring R of Type I_f, it is shown that the center of any factor ring of R is a factor ring of the center of R. These results are used to distinguish among the simple regular self-injective rings of Type II_f by their possible centers.

Mathematical Subject Classification

Primary: 16A30, 16A30

Secondary: 16A52, 16A48

Milestones

Received: 15 August 1977

Revised: 19 September 1977

Published: 1 June 1978