Rad−⊕−supplemented lattices

Abstract

. In this work, we define Rad −⊕− supplemented and strongly Rad −⊕− supplemented lattices and give some properties of these lattices. We generalize some properties of Rad − ⊕ − supplemented modules to lattices. Let L be a lattice and 1 = a 1 ⊕ a 2 ⊕ ... ⊕ a n with a 1 , a 2 ,..., a n ∈ L . If a i / 0 is Rad −⊕− supplemented for every i = 1 , 2 ,..., n , then L is also Rad −⊕− supplemented. Let L be a distributive Rad −⊕− supplemented lattice. Then 1 / u is Rad −⊕− supplemented for every u ∈ L . We also define completely Rad −⊕− supplemented lattices and prove that every Rad −⊕− supplemented lattice with SSP property is completely Rad −⊕− supplemented.