RAD− ⊕ −SUPPLEMENTED LATTICES.

In this work, we define Rad− ⊕ −supplemented an d strongly Rad− ⊕ −supplemented lattices an d give some properties of these lattices. We generalize some properties of Rad− ⊕ −supplemented modules to lattices. Let L be a lattice an d 1 = a1 ⊕a2 ⊕. . .⊕an with a1, a2, . . ., an ∈ L. If ai /0 is Rad− ⊕ − supplemented for every i = 1, 2, . . ., n, then L is also Rad− ⊕ − supple- mented. 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 an d prove that every Rad− ⊕ −supplemented lattice with SSP property is completely Rad− ⊕ − supplemented. [ABSTRACT FROM AUTHOR]