Zeitschrift für verallgemeinerte Lügentheorie und -anwendungen

Commutativity and ideals in algebraic crossed products

Abstract

Johan OINERT and Sergei D. SILVESTROV

We investigate properties of commutative subrings and ideals in non-commutative algebraic crossed products for actions by arbitrary groups. A description of the commutant of the coecient subring in the crossed product ring is given. Conditions for commutativity and maximal commutativity of the commutant of the coecient subring are provided in terms of the action as well as in terms of the intersection of ideals in the crossed product ring with the coecient subring, specially taking into account both the case of coecient rings without non-trivial zero-divisors and the case of coecient rings with non-trivial zero-divisors.