Cofinitely ⊕-Supplemented Lattices

Abstract

In this work, cofinitely circle plus-supplemented and strongly cofinitely circle plus-supplemented lattices are defined and investigated some properties of these lattices. Let L be a lattice and 1 = circle plus a(i) with a(i) is an element of L. If a(i)/0 is cofinitely circle plus-supplemented for every i is an element of I, then L is also cofinitely circle plus-supplemented. Let L be a distributive lattice and 1 = a(1) circle plus a(2) with a(1), a(2) is an element of L. If a(1)/0 and a(2)/0 are strongly cofinitely circle plus-supplemented, then L is also strongly cofinitely circle plus-supplemented. Let L be a lattice. If every cofinite element of L lies above a direct summand in L, then L is cofinitely circle plus-supplemented.