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.