Equiprime Ideals and Equiprime Semimodules in Boolean Like Semirings

Abstract

In this paper, the concepts of equiprime ideals and equiprime semi-modules in Boolean like semirings (now onwards denote ℜB) are introduced and illustrated with examples. It is established that if Ҏ is the equiprime ℜB–Ideal of the ℜB –module Ń then (Ҏ: Ń) is equiprime ideal of ℜB. Also it is approved that if Ń is an equiprime ℜB–module then (0: Ń) is an equiprime ideal of ℜB. Also, an important characterization of the equiprime ideal of ℜB in the semimodule structure over ℜB is put forward. Using this result, it can be proved that ℜB is equiprime if there exists a faithful equiprime ℜB–module Ń. Finally, it is proved that if Ń is an equiprime ℜB–module and Ϯ is an invariant subgroup of ℜB such that Ϯ is not contained in (0: Ń), then Ń is an equiprime Ϯ–module. Mathematics Subject Classification: 16Y30, 16Y80.