Cofinitely Supplemented Modular Lattices
ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING, cilt.36, sa.6, ss.919-923, 2011 (SCI-Expanded, Scopus)
- 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.