Ideal Theory of Sum-Ordered Partial Semirings

Partially dened innitary operations occur in the contexts ranging from integration theory to programming language semantics. The study of pfn(D;D), Mfn(D;D) and Mset(D;D) play an important role in the theory of computer science, and to abstract these structures Manes and Benson introduced the notion of sum-ordered partial semiring(so-ring). In view of ordering and partial addition in the so-ring, i obtained a phi-representation, developed an ideal theory of so-rings and studied partial semimodules over partial semirings in detail. This text book is helpful to the beginners of Partial semirings.