Generalizations of supplemented lattices
Shriram Khanderao Nimbhorkar, Deepali B. Banswal · AKCE International Journal of Graphs and Combinatorics · 2018
Some generalizations of the concept of a supplemented lattice, namely a soc-supplemented-lattice, soc-amply-supplemented-lattice, soc-weak-supplemented-lattice, soc-⊕-supplemented-lattice and completely soc-⊕-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-⊕-supplemented-lattice satisfying the summand intersection property (SIP), then L is a completely soc-⊕-supplemented-lattice.