Properties of hybrid ideals of rings

Abstract

The nature of universe problems is pretty ambiguous in almost all disciplines. To overcome the uncertainties, fuzzy set theory was developed. Later, mathematicians developed new concept, hybrid structures. The main aim of this paper is to study about hybrid structures in rings. The ideas of hybrid ideals, hybrid duo and hybrid prime ideals of rings are presented in this paper and investigate its properties. We found an equivalent claims for a ring to be regular and intra-regular. Further, we prove that hybrid product of hybrid right ideal and hybrid left ideal will coincide with hybrid intersection of hybrid right ideal and hybrid left ideal under certain condition. Moreover, we examine results related to hybrid prime ideals in rings.