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Some results on CLESS lattices. (English) Zbl 1454.06007
Summary: We introduce the concept of a CLESS lattice which is a generalization of the concept of an extending lattice (or a CS lattice). We study relationship between various generalizations of the concept of an extending lattice namely, CLS lattice, CLESS lattice and CESS lattice. We also prove that, if \(a\), \(b\) are direct summands of 1 which are CLESS elements then 1 is a CLESS element.
MSC:
06C20 Complemented modular lattices, continuous geometries
06C05 Modular lattices, Desarguesian lattices
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