Group Corings
نویسندگان
چکیده
We introduce group corings, and study functors between categories of comodules over group corings, and the relationship to graded modules over graded rings. Galois group corings are defined, and a Structure Theorem for the G-comodules over a Galois group coring is given. We study (graded) Morita contexts associated to a group coring. Our theory is applied to group corings associated to a comodule algebra over a Hopf group coalgebra.
منابع مشابه
Comatrix Corings and Galois Comodules over firm rings
Galois corings with a group-like element [4] provide a neat framework to understand the analogies between several theories like the Faithfully Flat Descent for (noncommutative) ring extensions [26], Hopf-Galois algebra extensions [27], or noncommutative Galois algebra extensions [23, 15]. A Galois coring is isomorphic in a canonical way to the Sweedler’s canonical coring A ⊗B A associated to a ...
متن کاملOn Coinduction Functors between Categories of Comodules for Corings
In this note we consider different versions of coinduction functors between categories of comodules for corings induced by a morphism of corings. In particular we introduce a new version of the coinduction functor in the case of locally projective corings as a composition of suitable “Trace” and “Hom” functors and show how to derive it from a more general coinduction functor between categories ...
متن کاملThe Bicategory of Corings
To a B-coring and a (B, A)-bimodule that is finitely generated and projective as a right A-module an A-coring is associated. This new coring is termed a base ring extension of a coring by a module. We study how the properties of a bimodule such as separability and the Frobenius properties are reflected in the induced base ring extension coring. Any bimodule that is finitely generated and projec...
متن کاملOn comatrix corings and bimodules
To any bimodule which is finitely generated and projective on one side one can associate a coring, known as a comatrix coring. A new description of comatrix corings in terms of data reminiscent of a Morita context is given. It is also studied how properties of bimodules are reflected in the associated comatrix corings. In particular it is shown that separable bimodules give rise to coseparable ...
متن کاملGalois Corings and a Jacobson-Bourbaki type Correspondence
The Jacobson-Bourbaki Theorem for division rings was formulated in terms of corings by Sweedler in [14]. Finiteness conditions hypotheses are not required in this new approach. In this paper we extend Sweedler’s result to simple artinian rings using a particular class of corings, comatrix corings. A Jacobson-Bourbaki like correspondence for simple artinian rings is then obtained by duality.
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ورودعنوان ژورنال:
- Applied Categorical Structures
دوره 16 شماره
صفحات -
تاریخ انتشار 2008