A note on \(\Gamma\)-rings (Q795910)

Let M be a \(\Gamma\)-ring. If A is any ideal of M, the radical \(r_ g(A)\) of A is the set of all elements x of M such that every g-system containing x contains an element of A. \textit{D. F. Hsu} [in Math. Jap. 21, 455-460 (1976; Zbl 0356.16014)], proved that \(r_ g(A)\) is the intersection of all g-prime ideals containing A. In this paper, the author introduces the notion of g-half prime ideals in \(\Gamma\)-rings and proves that an ideal A of the \(\Gamma\)-ring is g-half prime if and only if \(A=r_ g(A)\).