Generalized supplemented lattices

WOS: 000441460300011 In this work, we define (amply) generalized supplemented lattices and investigate some properties of these lattices. In this paper, all lattices are complete modular lattices with the smallest element 0 and the greatest element 1. Let L be a lattice, 1 = a(1) v a(2) v ... v a(n) and the quotient sub lattices a(1)/0, a(2)/0,..., a(n)/ 0 be generalized supplemented, then L is generalized supplemented. If L is an amply generalized supplemented lattice, then for every a is an element of L, the quotient sublattice 1 /a is amply generalized supplemented.