This paper is concerned with what, for lack of a better name, the author proposes to call geometric modules over a field k. These modules are defined as follows. A geometric module M consists of a vector space, also denoted by M, over k, together with a ring of linear transformations A of M into itself subject to the following conditions:

(i) A is a homomorphic image of the ring Sn = k[X1, …, Xn] of polynomials in n indeterminates X1, …, Xn for some value of n;

(ii) M, considered as an A-module, is finitely generated.