On Essential and Closed Fuzzy Ideals of a Semiring

Abstract

In this paper, existence of essential fuzzy ideal of a semiring S is shown and some of the properties of these ideals are investigated. The study of essentiality helps to develop the concepts like closed fuzzy ideal and relative fuzzy complement of S. Fuzzy ideal µ of S ( or δ) is said to be closed ideal of S ( or δ) if µ has no non-constant (proper) essential extension. Various results on closed fuzzy ideal of S are studied. Also relation between complementary summand and relative complement is established.