MISKOLC MATHEMATICAL NOTES, vol.21, no.2, pp.993-999, 2020 (SCI-Expanded)
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).