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Rational Modules for Corings Jawad Y. Abuhlail

Summary: Rational Modules for Corings
Jawad Y. Abuhlail
Mathematics Department
Birzeit University
P.O.Box 14, Birzeit - Palestine
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´omez-Torricillas and J. Lobillo to the so called rational pairings over a commutative
ground ring R to study the interplay between the comodules of an R-coalgebra C and
the modules of an R-algebra A that admits an R-algebra 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. Doi-Koppinen modules, alternative
Doi-Koppinen modules) generalizing results of Y. Doi , M. Koppinen and C. Menini
et al.


Source: Abuhlail, Jawad Younes - Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals


Collections: Mathematics