Module of covariants

In algebra, given an algebraic group G, a G-module M and a G-algebra A, all over a field k, the module of covariants of type M is the ${\displaystyle A^{G}}$-module

${\displaystyle (M\otimes _{k}A)^{G}.}$

where ${\displaystyle -^{G}}$ refers to taking the elements fixed by the action of G; thus, ${\displaystyle A^{G}}$ is the ring of invariants of A.