Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/4941
Title: Cofinitely supplemented modular lattices
Authors: Alizade, Rafail
Toksoy, Sultan Eylem
Keywords: Ample supplement
Amply cofinitely supplemented lattice
Cofinite element
Cofinitely supplemented lattice
Issue Date: Oct-2011
Publisher: Springer Verlag
Source: Alizade, R., and Toksoy, S.E. (2011). Cofinitely supplemented modular lattices. Arabian Journal for Science and Engineering, 36(6), 919-923. doi:10.1007/s13369-011-0095-z
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 v b there exists an element c of b/0 such that a v c 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.
URI: http://doi.org/10.1007/s13369-011-0095-z
http://hdl.handle.net/11147/4941
ISSN: 1319-8025
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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