Cofinitely Supplemented Modular Lattices


Alizade R., Toksoy S. E.

ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING, cilt.36, sa.6, ss.919-923, 2011 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 36 Sayı: 6
  • Basım Tarihi: 2011
  • Doi Numarası: 10.1007/s13369-011-0095-z
  • Dergi Adı: ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.919-923
  • Anahtar Kelimeler: Cofinite element, Ample supplement, Amply supplemented lattice, Cofinitely supplemented lattice, Amply cofinitely supplemented lattice
  • Hacettepe Üniversitesi Adresli: Hayır

Özet

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.