Generalizations of supplemented lattices

Peer review under responsibility of Kalasalingam University.

Abstract

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.

Keywords:

• Modular lattice
• Supplemented lattice
• Soc-supplemented-lattice
• Soc-amply-supplemented-lattice
• Soc-weak-supplemented-lattice

Notes

Peer review under responsibility of Kalasalingam University.