Generalized supplemented lattices
Çiğdem Biçer, Celıl Nebıyev, Ali Pancar · Miskolc mathematical notes/Mathematical notes · 2018
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 D a 1 _ a 2 _ : : : _ a n and the quotient sublattices 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 2 L, the quotient sublattice 1=a is amply generalized supplemented.