Study residuated lattice via some elements

Abstract

In this paper, the notions of distributive, standard and neutral elements in residuated lattices were introduced and relationships between them were investigated. Also we study the sets of distributive, standard and neutral elements in residuated lattices. Then we show that under some conditions, the sets of distributive, standard and neutral elements in residuated lattices become a $MTL$-algebra. Finally, special elements of type 2 in residuated lattices were introduced.