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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 (CC BY 3.0).

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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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