Essential supplemented lattices

Abstract

Let L be a complete modular lattice. If every essential element of L has a supplement in L, then L is called an essential supplemented (or briefly e-supplemented) lattice. In this work some properties of these lattices are investigated. Let L be a complete modular lattice and 1 = a(1)Va(2)V...Va(n) with a(i) is an element of L(1 <= i <= n). If ai/0 is e-supplemented for every i = 1,2, ..., n, then L is also e-supplemented. If L is e-supplemented, then 1/a is also e-supplemented for every a is an element of L.