Pseudo-irreducible ideals of residuated lattices

Abstract

In this article, the concept of pseudo-irreducible ideals in a residuated lattice is introduced and we consider its relationship with some important concepts of residuated lattices such as prime ideal and maximal ideal. Then using this concept, we define and study complete comaximal decomposition in residuated lattices. In particular, we characterize residuated lattices whose proper ideals can be written as an intersection of pairwise comaximal of finitely many pseudo-irreducible ideals. MSC(2010): 08A72, 08A99, 03G25.