 
Summary: Rational Modules for Corings
Jawad Y. Abuhlail
Mathematics Department
Birzeit University
P.O.Box 14, Birzeit  Palestine
jabuhlail@birzeit.edu
Abstract
The so called dense pairings were studied mainly by D. Radford in his work
on coreflexive coalegbras over fields. They were generalized in a joint paper with J.
G´omezTorricillas and J. Lobillo to the so called rational pairings over a commutative
ground ring R to study the interplay between the comodules of an Rcoalgebra C and
the modules of an Ralgebra A that admits an Ralgebra morphism : A C. Such
pairings, satisfying the so called condition, were called in the author's dissertation
measuring pairings and can be considered as the corner stone in his study of
duality theorems for Hopf algebras over commutative rings. In this paper we lay
the basis of the theory of rational modules of corings extending results on rational
modules for coalgebras to the case of arbitrary ground rings. We apply these results
mainly to categories of entwined modules (e.g. DoiKoppinen modules, alternative
DoiKoppinen modules) generalizing results of Y. Doi , M. Koppinen and C. Menini
et al.
