A Galois-type correspondence theory for actions of finite-dimensional pointed Hopf algebras on prime algebras (Q1305445)

The author gives a Galois correspondence for \(X\)-outer actions of a finite-dimensional Hopf algebra \(H\) over a field \(k\) on a prime algebra \(R\). This generalizes results of \textit{S. Montgomery} and \textit{D. S. Passman} [Rocky Mt. J. Math. 14, 305-318 (1984; Zbl 0541.16032)] and of \textit{V. K. Kharchenko} [Automorphisms and derivations of associative rings, Kluwer Academic, Dordrecht (1991; Zbl 0746.16002)] in the group case and of Kharchenko [op. cit.] in the case of restricted Lie algebras. The main theorem is for \(k\) of characteristic zero, \(H\) pointed. Let \(K\) be the center of the Martindale ring of quotients of \(R\). Then there is a one-to-one correspondence between the set of rationally complete intermediate subalgebras of \(R\) and the set of right subcomodule algebras of \(K\#H\) containing \(K\).