Integral ideals and maximal ideals in BL-algebras

Abstract

In this paper, we introduce the concept of integral ideals in BL-algebras. With respect to concept, we give some related results. In particular, we prove that an ideal is integral ideal if and only if is Boolean and (prime) maximal ideal. Also, we prove that a BL-algebra is an integral BL-algebra if and only if trivial ideal is an integral ideal. Moreover, we study relation between integral ideals and obstinate filters in BL-algebras by using the set of complement elements. Also, we describe relationship between maximal ideals in BL-algebras and locally finite MV-algebras.