Generalization of Cofinitely Supplemented Modules To Lattices

Abstract

In this thesis we study how to extend the notion of co¯nitely supplemented module to lattice theory. A submodule N of a module M is called co¯nite if the factor module M/N is ¯nitely generated and we say that M is a co¯nitely supplemented module if every co¯nite submodule of M has a supplement. We analogously de¯ne the notions of co¯nite element and co¯nitely supplemented lattice for lattices. Inspired by the similarities between the properties of modules and modular lattices, we obtain results for co¯nitely supplemented modular lattices, analogous to results for co¯nitely supplemented modules