Folding Theory for Integral and Boolean Ideals in BL-algebras

In this paper, we introduce the concepts of n-fold integral ideals and n-fold Boolean ideals in BL-algebras. 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.