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Mohssin Zarouali-Darkaoui 《代数通讯》2013,41(2):689-724
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. 相似文献
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Mohssin Zarouali-Darkaoui 《代数通讯》2013,41(12):4018-4031
We introduce and study the Picard group of a coring. We give an exact sequence relating the Picard group of a coring and its automorphisms generalizing the known exact sequences associated to an algebra and a coalgebra over a field. We also extend to corings the Aut–Pic property and we give some new corings satisfying this property. 相似文献
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Mohssin Zarouali-Darkaoui 《代数通讯》2013,41(10):3912-3943
We extend the comatrix coring to the case of a quasi-finite bicomodule. We also generalize some of its interesting properties. We study equivalences 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. We apply our results to corings coming from entwining structures and graded structures, and we obtain new results in the setting of entwining structures and in the graded ring theory. 相似文献
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