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Miskolc Mathematical Notes, cilt.27, sa.1, ss.89-95, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 27 Sayı: 1
- Basım Tarihi: 2026
- Doi Numarası: 10.18514/mmn.2026.5054
- 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.89-95
- Anahtar Kelimeler: lattices, radical, small elements, supplemented lattices
- Ondokuz Mayıs Üniversitesi Adresli: Evet
Özet
In this paper, all lattices are complete modular lattices with the greatest element 1 and the smallest element 0. Let L be a lattice, a ∈ L and a ≤ r(L). If a ∈ r(L)/0, then a is called an r-small (or r-superfluous) element of L and denoted by a ∈_r L. In this work, some properties of these elements are investigated. This concept is a generalization of an r-small submodule of any module. It is clear that every r-small element is small. But the converse of this statement is not true in general. Let L be a lattice, a ∈ r(L)/0 and r(L) be a supplement element in L. Then a ∈ L if and only if a ∈_r L. Let L be a lattice, a ∈ L and b ∈_r L. Then a ∈_r L if and only if a ∧ b ∈_r 1/b.