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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 C-Galois extensions over commutative rings.
Our approach is similar to that of Y. Doi and A. Masuoka in their work on (cleft)
H-Galois 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
C-comodule through A : A - AA C C, a xa for some group-like 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 A-ring
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