COFINITELY RADICAL SUPPLEMENTED AND COFINITELY WEAK RADICAL SUPPLEMENTED LATTICES

Nebiyev C., Okten H. H.

MISKOLC MATHEMATICAL NOTES, vol.21, no.2, pp.993-999, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 21 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.18514/mmn.2020.3219
  • Journal Name: MISKOLC MATHEMATICAL NOTES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.993-999
  • Keywords: lattices, small elements, supplemented lattices, generalized (radical) supplemented lattices
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

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).