Some Special Classes of Semirings

Advanced Algebra plays a key role in modern mathematics and a semiring is one of the important algebraic structure used in advanced algebra. The theory of semiring can be treated as a common generalization of the theories of associative rings and distributive lattices. Over the past several years, semirings have been studied by various researchers either to extend techniques coming from ring theory and semigroup theory or in connection with applications in different branches of applied mathematics and theoretical computer science. In this treatise we present the algebraic theory of semirings and study some properties of many important radical classes such as singular, strong, stable, normal radical classes of semirings. We also introduce and study the properties of 2-primal semiring and NI semiring.