Journal article
Co-Frobenius corings and adjoint functors
Journal of pure and applied algebra, Vol.212(9), pp.2027-2058
09/01/2008
DOI: 10.1016/j.jpaa.2007.11.015
Abstract
We study co-Frobenius and more generally quasi-co-Frobenius corings over arbitrary base rings and over PF base rings in particular. We generalize some results about co-Frobenius and quasi-co-Froben ius coalgebras to the case of non-commutative base rings and give several new characterizations for co-Frobenius and more generally quasi-co-Frobenius corings, some of them are new even in the coalgebra situation. We construct Morita contexts to study Frobenius properties of corings and a second kind of Morita contexts to study adjoint pairs. Comparing both Morita contexts, we obtain our main result that characterizes quasi-coFrobenius corings in terms of a pair of adjoint functors (F, G) such that (G, F) is locally quasi-adjoint in a sense defined in this note. (c) 2008 Elsevier B. V. All rights reserved.
Details
- Title: Subtitle
- Co-Frobenius corings and adjoint functors
- Creators
- M. C Iovanov - State University of New YorkJ Vercruysse - Vrije Universiteit Brussel
- Resource Type
- Journal article
- Publication Details
- Journal of pure and applied algebra, Vol.212(9), pp.2027-2058
- DOI
- 10.1016/j.jpaa.2007.11.015
- ISSN
- 0022-4049
- eISSN
- 1873-1376
- Publisher
- ELSEVIER SCIENCE BV
- Number of pages
- 32
- Language
- English
- Date published
- 09/01/2008
- Academic Unit
- Mathematics
- Record Identifier
- 9984240763702771
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