ON AMPLY g-SUPPLEMENTED LATTICES
Palestine Journal of Mathematics, vol.11, no.Special Issue 2, pp.37-40, 2022 (Scopus)
- Publication Type: Article / Article
- Volume: 11 Issue: Special Issue 2
- Publication Date: 2022
- Journal Name: Palestine Journal of Mathematics
- Journal Indexes: Scopus
- Page Numbers: pp.37-40
- Keywords: Essential Elements, g-Supplemented Lattices, Lattices, Small Elements
- Ondokuz Mayıs University Affiliated: Yes
Abstract
In this work, all lattices are complete modular lattices with the greatest element 1 and the smallest element 0. Let L be a lattice and a ∈ L. If for every b ∈ L such that a ∨ b = 1, a has a g-supplement x in L such that x ≤ b, then we say a has ample g-supplements in L. If every element of L has ample g-supplements in L, then L is called an amply g-supplemented lattice (See [7]). In this work, some properties of these lattices are investigated.