A BROWN-McCOY RADICAL FOR T-RINGS

Abstract

A notion of G-regularity is introduced for a Γ-ring M, and from this notion a Brown-McCoy radical, B(M) is defined. B(M) is shown to be a radical in the sense of Kurosh and Amitsur, and analogies of various well-known results on the Brown-McCoy radical of a ring are proved. A “right” Brown McCoy radical, B'(M) can also be defined. In general, B(M) • B'(M).