Module of covariants for a linear representation

Definition
The module of covariants for a linear representation of $$G$$ over a vector space $$V$$ over a field $$k$$, is the ring $$k[V]$$ viewed as a module over the invariant subring $$k[V]^G$$. When $$V = k^n$$, $$k[V]$$ is the polynomial ring in $$n$$ variables and $$k[V]^G$$ is the subring comprising those polynomials that are invariant under the action of $$G$$.