Abstract
We show the close connection between apparently different Galois theories for comodules introduced recently in [J. Gómez-Torrecillas and J. Vercruysse, Comatrix corings and Galois Comodules over firm rings, Algebr. Represent. Theory, 10 (2007), 271–306] and [Wisbauer, On Galois comodules, Comm. Algebra 34 (2006), 2683–2711]. Furthermore we study equivalences between categories of comodules over a coring and modules over a firm ring. We show that these equivalences are related to Galois theory for comodules.
Similar content being viewed by others
References
Dăscălescu, S., Năstăsescu, C., Raianu, Ş.: Hopf Algebras, Marcel Dekker Inc., New York, 2001
Caenepeel, S.: Galois corings from the descent theory point of view. Fields Inst. Comm, 43, 163–186 (2004)
Wisbauer, R.: From Galois field extensions to Galois comodules, Advances in ring theory, World Sci. Publ., Hackensack, NJ, 2005, 263–281
Brzeziński, T.: The structure of corings. Induction functors, Maschke-type theorem, and Frobenius and Galois properties. Algebr. Representat. Theory, 5, 389–410 (2002)
El Kaoutit, L., Gómez-Torrecillas, J.: Comatrix corings: Galois corings, Descent Theory, and a Structure Theorem for Cosemisimple corings. Math. Z., 244, 887–906 (2003)
Gómez-Torrecillas, J., Vercruysse, J.: Comatrix corings and Galois Comodules over firm rings. Algebr. Represent. Theory, 10, 271–306 (2007)
Caenepeel, S., De Groot, E., Vercruysse, J.: Constructing infinite Comatrix Corings from colimits. Appl. Categ. Structures, 14, 539–565 (2006)
El Kaoutit, L., Gómez-Torrecillas, J.: Infinite comatrix corings. Int. J. Res. Notices, 39, 2017–2037 (2004)
Wisbauer, R.: On Galois comodules. Comm. Algebra, 34, 2683–2711 (2006)
Brzeziński, T., Wisbauer, R.: Corings and comodules, London Math. Soc. Lect. Note Ser., 309, Cambridge University Press, Cambridge, 2003
Wisbauer, R.: Foundations of module and ring theory, Gordon and Breach, Philadelphia, 1991
Brzeziński, T., Gómez-Torrecillas, J.: On comatrix corings and bimodules. K-Theory, 29, 101–115 (2003)
Grandjean, F., Vitale, E. M.: Morita equivalence for regular algebras. Cahiers de Topology et Geometrie Differentielle, XXXIX, 137–153 (1998)
Stenström, B.: Rings of Quotients, Springer, Berlin, 1975
Mac Lane, S.: Categories for the working mathematician, second edition. Graduate Texts in Mathematics, 5, Springer Verlag, Berlin, 1997
Barr, M., Wells, C.: Toposes, Triples and Theories, Available at, http://www.cwru.edu/artsci/math/wells/pub/ttt.html http://www.cwru.edu/artsci/math/wells/pub/ttt.html.
Zimmermann-Huisgen, B.: Pure submodules of direct products of free modules. Math. Ann., 224 233–245 (1976)
Vercruysse, J.: Local units versus local projectivity. Dualisations: Corings with local structure maps. Comm. Algebra, 34, 2079–2103 (2006)
Gómez-Torrecillas, J.: Comonads and Galois Corings. Appl. Categ. Structures, 14, 579–598 (2006)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Vercruysse, J. Equivalences between categories of modules and categories of comodules. Acta. Math. Sin.-English Ser. 24, 1655–1674 (2008). https://doi.org/10.1007/s10114-007-6455-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10114-007-6455-7