Some Structures of Hemirings

Abstract

Hemirings appear in a natural manner, in some applications to the theory of automata, the theory of formal languages, graph theory, design theory and combinatorial geometry. Recently, the notions of hemirings with special structures were introduced. But still now there are no complete structural properties of hemirings. In this paper we try to investigate some structures of hemirings. This is done by introducing some examples of hemirings.

Semirings of graphs: homomorphisms and applications in network problems

“…Some authors consider semirings to posses neutral elements with respect to both the binary operations defined on it (see [6]). In some literatures, the authors consider algebraic structures with two binary operations, addition and multiplication such that the structure is additively commutative monoid, multiplicatively semigroup and multiplication distributes over addition from both left and right, called "hemirings" (see [1]). It is worth mentioning that this nomenclature is not 100% settled yet.…”