Generalizations of supplemented lattices

Abstract

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 is a soc--supplemented-lattice satisfying the summand intersection property (SIP), then is a completely soc--supplemented-lattice.

Keywords

• modular lattice
• supplemented lattice
• soc-supplemented-lattice
• soc-amply-supplemented-lattice
• soc-weak-supplemented-lattice