Introduction to Riesz \(l G\) -module

Abstract

Action of an \(l\)-group on a vector lattice (Riesz space) is defined and the abstract structure of the space thus formed is termed as a Riesz \(l G\)-module. Submodules namely, Riesz \(lG\)-submodule, convex Riesz \(lG\)-submodule are defined and properties are studied. A homomorphism called \(RlG\) - module homomorphism between two Riesz \(lG\) - modules is defined and properties are studied. An isomorphism namely, \(RlG\) module isomorphism is also defined.