Cofinitely soc-supplemented lattices

Ismael Akray & Haval M. Mohammed Salih

Department of Mathematics, Faculty of Science, Soran University/Erbil/Iraq
Department of Mathematics, Faculty of Science, Soran University/Erbil/Iraq



In this paper, we define Rad-supplemented lattice and its dual soc-supplemented lattice. Furthermore, we show that in compactly generated lattices the first one is equivalent to supplemented lattice. Also, we study some properties of soc-supplemented lattices. Finally, we define cofinitely soc-supplemented lattice (briefly css-lattice) and proved that an arbitrary join of css-lattices is a css-lattice.

Key Words:
Supplemented lattice; radical and socle of lattice; cofinite element 


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