N-Fold integral ideals and n-fold Boolean ideals in BL-algebras

Abstract

In this paper, we introduce the concepts of n-fold integral ideals and n-fold Boolean ideals in BL-algebras. With respect to concepts, we give some related results. In particular, we prove that an ideal is an n-fold integral ideal if and only if is an n-fold Boolean and (prime)maximal ideal. Also, we prove that a BL-algebra is an n-fold integral BL-algebra if and only if trivial ideal $$\{0\}$$ is an n-fold integral ideal. Moreover, we study relation between n-fold integral ideals and n-fold obstinate filters in BL-algebras by using the set of complement elements. Also, we describe relationship between n-fold Boolean ideals and n-fold positive implicative filters in BL-algebras.