Cofinitely radical supplemented and cofinitely weak radical supplemented lattices
Celıl Nebıyev, Hasan Hüseyın Ökten · Miskolc mathematical notes/Mathematical notes · 2020
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 ∈ L for every i ∈ I.If 1 = ∨ i∈I a i and a i /0 is cofinitely (weak) radical supplemented for every i ∈ I, then L is also cofinitely (weak) radical supplemented.Let L be a cofinitely (weak) radical supplemented lattice and a ∈ 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).