Centers of regular self-injective rings

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/, 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 11/ by their possible centers.All rings in this paper are associative with unit, and all ring maps are assumed to preserve the unit.