Ideal Theory of ��- SEMIRINGS

Ever since Nobusawa initiated the study of Γ−rings as a generalization of ring theory which enabled a multiplication of two matrices of same order and the composition of two homomorphisms from two algebraic structures A to B with the help of auxiliary operators (say Γ) several mathematicians enriched the theory of Γ−semirings as a generalization of the theory of Γ−rings and ternary rings. M.K. Sen initiated the study of Γ−semigroups. T.K.Dutta and several authors made extensive studies of Γ−semigroups. At this juncture inspired by the above mentioned studies the present author M. Murali Krishna Rao introduced the notion of Γ−semiring and studied extensively generalizing Γ−rings rings ternary semirings and semirings.