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Axioms 2012, 1(2), 173-185; doi:10.3390/axioms1020173

The Duality between Corings and Ring Extensions

1,*  and 2
1 Institute of Mathematics of the Romanian Academy, 21 Calea Grivitei Street, 010702 Bucharest, Romania 2 Department of Theoretical Physics and Computer Science, University of Łodz, Pomorska 149/153, 90-236, Łodz, Poland
* Author to whom correspondence should be addressed.
Received: 29 June 2012 / Revised: 24 July 2012 / Accepted: 30 July 2012 / Published: 10 August 2012
(This article belongs to the Special Issue Hopf Algebras, Quantum Groups and Yang-Baxter Equations)
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We study the duality between corings and ring extensions. We construct a new category with a self-dual functor acting on it, which extends that duality. This construction can be seen as the non-commutative case of another duality extension: the duality between finite dimensional algebras and coalgebra. Both these duality extensions have some similarities with the Pontryagin-van Kampen duality theorem.
Keywords: corings; ring extension; duality; Yang–Baxter equation corings; ring extension; duality; Yang–Baxter equation
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Nichita, F.F.; Zielinski, B. The Duality between Corings and Ring Extensions. Axioms 2012, 1, 173-185.

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