Cofinitely ⨁-supplemented lattices
Çiğdem Biçer, Celıl Nebıyev · Miskolc mathematical notes/Mathematical notes · 2020
In this work, cofinitely ⊕-supplemented and strongly cofinitely ⊕-supplemented lattices are defined and investigated some properties of these lattices.Let L be a lattice and 1 = ⊕ i∈I a i with a i ∈ L. If a i /0 is cofinitely ⊕-supplemented for every i ∈ I, then L is also cofinitely ⊕-supplemented.Let L be a distributive lattice and 1 = a 1 ⊕ a 2 with a 1 , a 2 ∈ L. If a 1 /0 and a 2 /0 are strongly cofinitely ⊕-supplemented, then L is also strongly cofinitely ⊕-supplemented.Let L be a lattice.If every cofinite element of L lies above a direct summand in L, then L is cofinitely ⊕-supplemented.