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Generalizations of supplemented lattices. (English) Zbl 1423.06025
Summary: Some generalizations of the concept of a supplemented lattice, namely a soc-supplemented-lattice, soc-amply-supplemented-lattice, soc-weak-supplemented-lattice, soc-\(\oplus\)-supplemented-lattice and completely soc-\(\oplus\)-supplemented-lattice are introduced. Various results are proved to show the relationship between these lattices. We have also proved that, if \(L\) is a soc-\(\oplus\)-supplemented-lattice satisfying the summand intersection property (SIP), then \(L\) is a completely soc-\(\oplus\)-supplemented-lattice.
MSC:
06C05 Modular lattices, Desarguesian lattices
06C15 Complemented lattices, orthocomplemented lattices and posets
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