GENERALIZED SUPPLEMENTED LATTICES

Bicer C., Nebiyev C., Pancar A.

MISKOLC MATHEMATICAL NOTES, vol.19, no.1, pp.141-147, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 19 Issue: 1
  • Publication Date: 2018
  • Doi Number: 10.18514/mmn.2018.1974
  • Journal Name: MISKOLC MATHEMATICAL NOTES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.141-147
  • Keywords: lattices, supplemented lattices, amply supplemented lattices, hollow lattices
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

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.