 
Summary: Morita Contexts for Corings and Equivalences
Jawad Y. Abuhlail
Mathematics Department
Birzeit University
P.O.Box 14, Birzeit  Palestine
jabuhlail@birzeit.edu
Abstract
In this note we study Morita contexts and Galois extensions for corings. For
a coring C over a (not necessarily commutative) ground ring A we give equivalent
conditions for MC to satisfy the weak. resp. the strong structure theorem. We
also characterize the so called cleft CGalois extensions over commutative rings.
Our approach is similar to that of Y. Doi and A. Masuoka in their work on (cleft)
HGalois extensions (e.g. [Doi94], [DM92]).
Introduction
Let C be a coring over a not necessarily commutative ring A and assume A to be a right
Ccomodule through A : A  AA C C, a xa for some grouplike element x C (see
[Brz02, Lemma 5.1]). In the first section we study from the viewpoint of Morita theory the
relationship between A and its subring of coinvariants B := AcoC
:= {b A  (b) = bx}.
We consider the Aring
