Essential supplemented lattices
Hasan Hüseyın Ökten, Ayten Peki̇n · Miskolc mathematical notes/Mathematical notes · 2020
Let L be a complete modular lattice.If every essential element of L has a supplement in L, then L is called an essential supplemented (or briefly e-supplemented) lattice.In this work some properties of these lattices are investigated.Let L be a complete modular lattice and 1 = a 1 ∨ a 2 ∨ ... ∨ a n with a i ∈ L (1 ≤ i ≤ n).If a i /0 is e-supplemented for every i = 1, 2, ..., n, then L is also e-supplemented.If L is e-supplemented, then 1/a is also e-supplemented for every a ∈ L.