SOME PROPERTIES OF WEAKLY G-SUPPLEMENTED LATTICES
Miskolc Mathematical Notes, cilt.27, sa.1, ss.275-281, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 27 Sayı: 1
- Basım Tarihi: 2026
- Doi Numarası: 10.18514/mmn.2026.5051
- Dergi Adı: Miskolc Mathematical Notes
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, MathSciNet, zbMATH, Directory of Open Access Journals, Academic Search Ultimate (EBSCO), East & Central Europe Database (ProQuest), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Sayfa Sayıları: ss.275-281
- Anahtar Kelimeler: g-small elements, g-supplemented lattices, lattices, small elements
- Ondokuz Mayıs Üniversitesi Adresli: Evet
Özet
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,b∈ L. If a⋁ b=1 and a⋀ b≪g L, then b is called a weak g-supplement of a in L. If every element of L has a weak g-supplement in L, then L is called a weakly g-supplemented lattice. In this work, some properties of these lattices are investigated. Let L be a lattice and a,b,c∈ L. If c≪ L, then b is a weak g-supplement of a in L if and only if b is a weak g-supplement of a⋁ c in L. Let L be a lattice and 1=a1⋁ a2⋁…⋁ an with ai∈ L (1≤ i≤ n). If ai/0 is weakly g-supplemented for every i=1,2,…,n, then L is also weakly g-supplemented. Let L be a weakly g-supplemented lattice. Then 1/a is weakly g-supplemented for every a∈ L. If L is a weakly g-supplemented lattice, then 1/rg(L) is complemented. Let L be a lattice. Then L is weakly g-supplemented if and only if for every a,b∈ L with 1=a⋁ b, a has a weak g-supplement c in L with c≤ b. Let L be a lattice and aβ*b in L. If a and b have weak g-supplements in L, then they have the same weak g-supplements in L.