Cofinitely Radical Supplemented and Cofinitely Weak Radical Supplemented Lattices

Abstract

In this work, cofinitely radical supplemented and cofinitely weak radical supplemented lattices are defined and some properties of them are investigated. Let L be a lattice, I be a nonempty index set and a(i) is an element of L for every i is an element of I. If 1 = boolean OR(i is an element of I )a(i) and a(i)/0 is cofinitely (weak) radical supplemented for every i c I, then L is also cofinitely (weak) radical supplemented. Let L be a cofinitely (weak) radical supplemented lattice and a is an element of L. Then 1/a is also cofinitely (weak) radical supplemented. Let L be a lattice. Then L is cofinitely weak radical supplemented if and only if every cofinite element of 1/r (L) is a direct summand of 1/r (L).