Morita Contexts for Corings and Equivalences

2003/02/01 by Jawad Abuhlail, Jawad Y. Abuhlail, Abuhlail, Jawad Y.
Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #Rings, Modules, and Algebras #math.QA #math.RA #msc:16D90 #msc:16S40 #msc:16W30

paper · pdf · doi:10.48550/arxiv.math/0302008

22 pages

arxiv created 2005/04/04 · arxiv updated 2009/11/30

Abstract

In this note we study Morita contexts and Galois extensions for corings. For a coring \QTRcalC over a (not necessarily commutative) ground ring A we give equivalent conditions for \QTRcalM^\QTRcalC to satisfy the weak. resp. the strong structure theorem. We also characterize the so called \QTRemcleftC\QTRem-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.

Related

• Galois corings applied to partial Galois theory
• Galois theory for comatrix corings: descent theory, Morita theory, Frobenius and separability properties
• Galois extensions over commutative and non-commutative base
• Morita Theory for corings and cleft entwining structures
• Corner replacement for Morita contexts