Lattice vector spaces and linear transformations

Abstract

This paper introduces the concept of lattice vector space and establishes many important results. Also, this paper deals with linear transformations on lattice vector spaces and discusses their elementary properties. We prove that every finite dimensional lattice vector space is isomorphic to [Formula: see text] and show that the set of all columns (or the set of all rows) of an invertible matrix over [Formula: see text] is a basis for [Formula: see text].