REGULARITY OF THE GENERALIZED CENTROID OF SEMI-PRIME GAMMA RINGS Ali Ozturk, Mehmet ; Jun, Young-Bae;
The aim of this note is to study properties of the generalized centroid of the semi-prime gamma rings. Main results are the following theorems: (1) Let M be a semi-prime -ring and Q a quotient -ring of M. If W is a non-zero submodule of the right (left) M-module Q, then 0. Furthermore Q is a semi-prime -ring. (2) Let M be a semi-prime -ring and the generalized centroid of M. Then is a regular -ring. (3) Let M be a semi-prime -ring and the extended centroid of M. If is a -field, then the -ring M is a prime -ring.