A NOTE ON THE g-PRIME RADICAL IN GAMMA RINGS

ABSTRACT

The g-prime radical of a Γ-ring M is equal to either the zero ideal or the prime radical of M. If the prime radical of M is a non-zero ideal, then the following three conditions are equivalent; (i) g-prime radical of M is equal to the prime radical of M; (ii) every g-prime ideal is a prime ideal; and (iii) every g-semiprime ideal is a semiprime ideal.