Martindale rings and $H$-module algebras with invariant characteristic polynomials

Under study is the category $\mathscr A$ of the possibly noncommutative $H$-module algebras that are mapped homomorphically onto commutative algebras. The $H$-equivariant Martindale ring of quotients $Q_H(A)$ is shown to be a finite-dimensional Frobenius algebra over the subfield of invariant elements $Q_H(A)^H$ and also the classical ring of quotients for $A$. We introduce a full subcategory $\widetilde{\mathscr A}$ of $\mathscr A$ such that the algebras in $\widetilde{\mathscr A}$ are integral over its subalgebras of invariants and construct a functor $\mathscr A\to\widetilde{\mathscr A}$, which is left adjoined to the inclusion $\widetilde{\mathscr A}\to\mathscr A$.