Cofinitely soc-supplemented lattices - Akray, Ismael; Salih, Haval M. Mohammed (Sulaimani Journal for Pure and Applied Sciences, 2016)
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.
Keywords: Supplemented lattice radical and socle of lattice cofinite element