Vol. 57, No. 2, 1975

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Semiprime rings with the singular splitting property

Mark Lawrence Teply

Vol. 57 (1975), No. 2, 575–579

A (right nonsingular) ring R is called a splitting ring if, for every right R-module M, the singular submodule Z(M) is a direct summand of M. If R is a semiprime splitting ring with zero right socle, then R contains no infinite direct sum of two-sided ideals. As applications of this result, the center of a semiprime splitting ring with zero socle is analyzed, and the study of splitting ring is completely reduced to the case where R is a prime ring. The center of a semiprime splitting ring is a von Neumann regular ring.

Mathematical Subject Classification
Primary: 16A12
Received: 18 November 1974
Published: 1 April 1975
Mark Lawrence Teply