Abstract
We investigate adjoint and Frobenius pairs between categories of comodules over rather general corings. We particularize to the case of the adjoint pair of functors associated to a morphism of corings over different base rings, which leads to a reasonable notion of Frobenius coring extension. When applied to corings stemming from entwining structures, we obtain new results in this setting and in graded ring theory.
ACKNOWLEDGMENTS
I would like to thank my advisor, Professor José Gómez-Torrecillas, for his assistance in the writing of this article, and for interesting discussions.
I would also like to express my deep gratitude to Professor Edgar Enochs for communicating the example of a commutative self-injective ring which is not coherent, and to Professor Tomasz Brzeziński for his assistance, for his careful reading of this article, and for his useful comments.
Finally, I wish to thank Editor Robert Wisbauer and the referee for some helpful suggestions.
Notes
Communicated by R. Wisbauer.