On semigamma bi- ideals in г- seminear-rings

The concept of bi-ideals for near- rings was introduced by T.Tamizh Chelvam and N.Ganesan [6]. Subsequently the notion of quasi ideals and bi-ideals in Г-near-rings was introduced by T.Tamizh Chelvam and N.Meenakumari [7]. An interesting special case of bi-ideals is given by the quasi-ideals of Steinfeld [5]. The concept of Г-seminear-rings was introduced by Kyung Ho Kim [3]. In this paper we introduce the notion of semigamma quasi-ideals, semigamma bi-ideals and b-simple Г- seminear-rings. Using the notion of semigamma bi-ideals, we show that the set of all semigamma bi-ideals of a Г- seminear-ring form a moore system. Also we proved that the intersection of a semigamma bi-ideals of Г- seminear-ring M and sub- Г- seminear-ring S is again a semigamma bi- ideal of S. We define b-simple Г- seminear-ring and prove certain equivalent conditions of Г- seminear-field. Throughout this paper, by a Г- seminear-ring M we shall mean a zero symmetric Г- seminear-ring.