Ideal Theory of ¿- SEMIRINGS

Ever since Nobusawa initiated the study of ¿¿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 ¿), several mathematicians enriched the theory of ¿¿semirings, as a generalization of the theory of ¿¿rings and ternary rings. M.K. Sen initiated the study of ¿¿semigroups. T.K.Dutta and several authors made extensive studies of ¿¿semigroups. At this juncture, inspired by the above mentioned studies, the present author M. Murali Krishna Rao, introduced the notion of ¿¿semiring and studied extensively, generalizing ¿¿rings, rings, ternary semirings and semirings.