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
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 Blattner-Montgomery
duality theorem to the case of arbitrary Noetherian ground rings.
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.
Cohen-Montgomery duality theorems [CM84]).
In [BM85] R. Blattner and S. Montgomery extended Cohen-Montgomery duality theo-
rems to the case of a Hopf R-algebra with bijective antipode acting on an R-algebra, where
R is a base field, providing an infinite version of the finite one achieved independently by