ON SUPPLEMENT ELEMENTS IN LATTICES

Nebiyev C.

MISKOLC MATHEMATICAL NOTES, cilt.20, sa.1, ss.441-449, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 20 Sayı: 1
  • Basım Tarihi: 2019
  • Doi Numarası: 10.18514/mmn.2019.2844
  • Dergi Adı: MISKOLC MATHEMATICAL NOTES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.441-449
  • Anahtar Kelimeler: lattices, small elements, supplemented lattices, complemented lattices
  • Ondokuz Mayıs Üniversitesi Adresli: Evet

Özet

In this work, some properties of supplement elements in lattices are investigated. Some relation between lying above and (weak) supplement elements also studied. Some properties of supplement submodules in modules which given in [8] are generalized to lattices. Let a be a supplement of b in a lattice L. If a/0 has at least one maximal (not equal a) element, then it is possible to define a bijective map between the maximal elements (not equal a) of a/0 and the maximal elements (not equal 1) of 1/b. Let a be a supplement element in a lattice L. If L is amply supplemented, then a/0 is also amply supplemented. If L is weakly supplemented, then a/0 is also weakly supplemented.