The complete comaximal decomposition in residuated lattices

Abstract

In this paper, we introduce the concept of pseudo-irreducible ideals in residuated lattices and obtain its relationship with important concepts such as prime ideals and maximal ideals in residuated lattices. We then use this concept to define and study complete comaximal decomposition in residuated lattices. Specifically, we characterize residuated lattices in which proper ideals can be expressed as the intersection of pairwise comaximal of finitely many pseudo-irreducible ideals.