Nonsingular Semiperfect CS-Rings
by
Pramod Kanwar
Truman State University
Coauthors: S. K. Jain, Sergio R. López-Permouth

In this paper we obtain the precise structure of right nonsingular semiperfect right CS-rings. Among other things it is shown that for a ring R, the following are equivalent: (a) R is an indecomposable right nonsingular semiperfect right CS-ring.(b) R is isomorphic to (M_ni×nj(D_ij)) where D_ii is a local domain contained in a division ring D, for i =/= j, D_ij is an additive subgroup of D. Furthermore, (i) for i <= j, D_ij =/= 0, (ii) for i > j if D_ij=0 then for all l >= i and m <= j, D_lm=0 and D_ml=D, (iii) if n_i > 1 then for every c in D either c in D_ii or c^-1 in D_ii, (iv) if for i =/= j, D_ij and D_ji are both nonzero then for every c in D either c in D_ij or c^-1 in D_ji, (v) the injective hull of D_ik as right D_kk-module is D. (c) R is isomorphic to (S_ij) where for each i, S_ii is a prime right nonsingular semiperfect right CS-ring, for i < j, S_ij consists of rectangular matrices over D of the appropriate size and for i > j, S_ij=0.In particular the classical ring of right quotients of a semiperfect right nonsingular right CS-ring is semiprimary.

Date received: March 23, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cabz-12.