Cofinitely Supplemented Modular Lattices


Alizade R., Toksoy S. E.

ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING, vol.36, no.6, pp.919-923, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 6
  • Publication Date: 2011
  • Doi Number: 10.1007/s13369-011-0095-z
  • Journal Name: ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.919-923
  • Keywords: Cofinite element, Ample supplement, Amply supplemented lattice, Cofinitely supplemented lattice, Amply cofinitely supplemented lattice
  • Hacettepe University Affiliated: No

Abstract

In this paper it is shown that a lattice L is a cofinitely supplemented lattice if and only if every maximal element of L has a supplement in L. If a/0 is a cofinitely supplemented sublattice and 1/a has no maximal element, then L is cofinitely supplemented. A lattice L is amply cofinitely supplemented if and only if every maximal element of L has ample supplements in L if and only if for every cofinite element a and an element b of L with a boolean OR b = 1 there exists an element c of b/0 such that a boolean OR c = 1 where c is the join of finite number of local elements of b/0. In particular, a compact lattice L is amply supplemented if and only if every maximal element of L has ample supplements in L.