GENERALIZED SUPPLEMENTED LATTICES

Bicer C., Nebiyev C., Pancar A.

MISKOLC MATHEMATICAL NOTES, cilt.19, sa.1, ss.141-147, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 19 Sayı: 1
  • Basım Tarihi: 2018
  • Doi Numarası: 10.18514/mmn.2018.1974
  • Dergi Adı: MISKOLC MATHEMATICAL NOTES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.141-147
  • Anahtar Kelimeler: lattices, supplemented lattices, amply supplemented lattices, hollow lattices
  • Ondokuz Mayıs Üniversitesi Adresli: Evet

Özet

In this work, we define (amply) generalized supplemented lattices and investigate some properties of these lattices. In this paper, all lattices are complete modular lattices with the smallest element 0 and the greatest element 1. Let L be a lattice, 1 = a(1) v a(2) v ... v a(n) and the quotient sub lattices a(1)/0, a(2)/0,..., a(n)/ 0 be generalized supplemented, then L is generalized supplemented. If L is an amply generalized supplemented lattice, then for every a is an element of L, the quotient sublattice 1 /a is amply generalized supplemented.