COFINITELY RADICAL SUPPLEMENTED AND COFINITELY WEAK RADICAL SUPPLEMENTED LATTICES

Nebiyev C., Okten H. H.

MISKOLC MATHEMATICAL NOTES, cilt.21, sa.2, ss.993-999, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 21 Sayı: 2
  • Basım Tarihi: 2020
  • Doi Numarası: 10.18514/mmn.2020.3219
  • Dergi Adı: MISKOLC MATHEMATICAL NOTES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Sayfa Sayıları: ss.993-999
  • Anahtar Kelimeler: lattices, small elements, supplemented lattices, generalized (radical) supplemented lattices
  • Ondokuz Mayıs Üniversitesi Adresli: Evet

Özet

In this work, cofinitely radical supplemented and cofinitely weak radical supplemented lattices are defined and some properties of them are investigated. Let L be a lattice, I be a nonempty index set and a(i) is an element of L for every i is an element of I. If 1 = boolean OR(i is an element of I )a(i) and a(i)/0 is cofinitely (weak) radical supplemented for every i c I, then L is also cofinitely (weak) radical supplemented. Let L be a cofinitely (weak) radical supplemented lattice and a is an element of L. Then 1/a is also cofinitely (weak) radical supplemented. Let L be a lattice. Then L is cofinitely weak radical supplemented if and only if every cofinite element of 1/r (L) is a direct summand of 1/r (L).