Amply essential supplemented lattices
Figen Eryılmaz, Celil Nebiyev, Hasan Hüseyin Ökten · Miskolc mathematical notes/Mathematical notes · 2025
In this work, amply essential supplemented (briefly, amply e-supplemented) lattices are defined and some properties of these lattices are investigated. All lattices are complete modular lattices with the greatest element 1 and the smallest element 0 in this work. Let L be a lattice. If b ∕ 0 is essential supplemented for every b ∈ L , then L is amply essential supplemented. Let L be an amply e-supplemented lattice, b be a supplement of a in L and b ⊴ L . Then b ∕ 0 is amply e-supplemented. Here also x ∕ 0 is amply supplemented for every e-supplement element x in L . Let L be a lattice. Then L is amply essential supplemented if and only if a ∧ b has a supplement in b ∕ 0 for every a ⊴ L and b ∈ L with 1 = a ∨ b . Let L be a lattice. If a ∧ b lies above an e-supplement element in L for every a , b ∈ L with a ⊴ L and 1 = a ∨ b , then L is amply e-supplemented.