Polar modules

Abstract

This paper is concerned with what, for lack of a better name, the author proposes to call geometric modules over a fieldk. These modules are defined as follows. A geometric moduleMconsists of a vector space, also denoted byM, overk, together with a ring of linear transformationsAofMinto itself subject to the following conditions:(i)Ais a homomorphic image of the ringSn=k[X1, …,Xn] of polynomials innindeterminatesX1, …,Xnfor some value ofn;(ii)M, considered as anA-module, is finitely generated.