Martindale rings and H-module algebras with invariant characteristic polynomials

Abstract

Under study is the category 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 à of A such that the algebras in à are integral over its subalgebras of invariants and construct a functor A → à which is left adjoined to the inclusion à → A. © 2012 Pleiades Publishing, Ltd.