On Fuzzy semihyperrings

Abstract

In this article we introduce the study of fuzzy semihyperrings and fuzzy R-semihypermodules, where R is a semihyperrings and R-semihypermodules are represntations of R. In particular, semihyperrings all of whose hyperideals are idempotent, called fully idempotent semihyperrings, are investigated in a fuzzy context. It is proved, among other results, that a semihyperring R is fully idempotent if and only if the lattics of fuzzy hyperideals of R is distributive under the sum and product of fuzzy hyperideals. It is also shown that the set of proper fuzzy prime hyperideals of a fully idempotent semihyperring R admits the structure of a topological space, called the fuzzy prime spectrum of R.