Valuation $\tau$-Semirings and Valuation $\tau$-Ideals

S. Sangwirotjanapat, S. Tipyota, S. Pianskool

Abstract

Valuation semigroups, valuation ideals of a semigroup and $\tau$-semirings have been studied as seen in [2] and [3]. T.K. Dutta and S.K. Sardar also showed that there always exist two particular operator semirings associated a given $\tau$-semiring. Besides, there are strong connections between subsets of these two semi-rings and their corresponding subsets in their associated $\tau$-semiring. We introduce the notion of valuation $\tau$-semirings and valuation $\tau$-ideals of a $\tau$-semiring. Studying these via the operator semirings, we obtained other relationship between $\tau$-semirings and their associated operator semirings in the valuation aspect.