circle plus-SUPPLEMENTED LATTICES

Abstract

In this work, circle plus-supplemented and strongly circle plus-supplemented lattices are defined and investigated some properties of these lattices. Let L be a lattice and 1 = a(1) circle plus a(2) circle plus ... circle plus a(n) with a(1), a(2), ..., a(n) is an element of L. If a(i)/0 is circle plus-supplemented for each i = 1, 2, ..., n, then L is also circle plus-supplemented. Let L be a distributive lattice and 1 = a(1) circle plus a(2) circle plus ... circle plus a(n) with a(1), a(2), ..., a(n) is an element of L. If a(i)/0 is strongly circle plus-supplemented for each i = 1, 2, ..., n, then L is also strongly circle plus-supplemented. A lattice L has (D1) property if and only if L is amply supplemented and strongly circle plus-supplemented.