 
Summary: Duality Theorems for Crossed Products over Rings
Jawad Y. Abuhlail
Department of Mathematical Sciences
King Fahd University of Petroleum & Minerals
31261 Dhahran  Saudi Arabia
abuhlail@kfupm.edu.sa
Abstract
In this note we improve and extend duality theorems for crossed products obtained
by M. Koppinen (C. Chen) from the case of base fields (Dedekind domains) to the case
of an arbitrary Noetherian commutative ground rings under fairly weak conditions.
In particular we extend an improved version of the celebrated BlattnerMontgomery
duality theorem to the case of arbitrary Noetherian ground rings.
Introduction
Crossed products in the theory of Hopf Algebras were presented independently by R. Blat
tner, M. Cohen, S. Montgomery [BCM86] and Y. Doi, M. Takeuchi [DT86]. The so called
duality theorems for crossed products have their roots in the theory of group rings (e.g.
CohenMontgomery duality theorems [CM84]).
In [BM85] R. Blattner and S. Montgomery extended CohenMontgomery duality theo
rems to the case of a Hopf Ralgebra with bijective antipode acting on an Ralgebra, where
R is a base field, providing an infinite version of the finite one achieved independently by
