COFINITELY circle plus-SUPPLEMENTED LATTICES


Bicer C., Nebiyev C.

MISKOLC MATHEMATICAL NOTES, vol.21, no.1, pp.81-89, 2020 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 21 Issue: 1
  • Publication Date: 2020
  • Doi Number: 10.18514/mmn.2020.2904
  • Journal Name: MISKOLC MATHEMATICAL NOTES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.81-89
  • Keywords: lattices, compact elements, small elements, supplemented lattices
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

In this work, cofinitely circle plus-supplemented and strongly cofinitely circle plus-supplemented lattices are defined and investigated some properties of these lattices. Let L be a lattice and 1 = circle plus a(i) with a(i) is an element of L. If a(i)/0 is cofinitely circle plus-supplemented for every i is an element of I, then L is also cofinitely circle plus-supplemented. Let L be a distributive lattice and 1 = a(1) circle plus a(2) with a(1), a(2) is an element of L. If a(1)/0 and a(2)/0 are strongly cofinitely circle plus-supplemented, then L is also strongly cofinitely circle plus-supplemented. Let L be a lattice. If every cofinite element of L lies above a direct summand in L, then L is cofinitely circle plus-supplemented.