Some results on primary filters in BL-algebras

Abstract

In this article, with the aim of further investigating BL-algebras, the concepts of a prime less filter is introduced and discussed. Also, for the faster study of prime less filters in BL-algebras, some equivalent conditions are obtained. We prove some relations between this filter and other types of filters in BL-algebras. Also, some results that proven for prime filters in BL-algebras, to the case of prime less filters are proven. In this way, we find new properties for the primary filters in BL-algebras. Also, the notions of prime less BL-algebras (Pls–BL-algebras) are introduced and investigated.