Corings with Decomposition and Semiperfect Corings
نویسندگان
چکیده
منابع مشابه
On Corings and Comodules
It is shown that the categories of R-coalgebras for a commutative unital ring R and the category of A-corings for some R-algebra A as well as their respective categories of comodules are locally presentable.
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The notion of a coring was introduced by M. E. Sweedler in [20] with the objective of formulating and proving a predual to the Jacobson-Bourbaki theorem for extensions of division rings. A fundamental argument in [20] is the following: given division rings E ⊆ A, each coideal J of the A–coring A ⊗E A gives rise to a factor coring C = A ⊗E A/J . If g ∈ C denotes the group-like element 1 ⊗E 1 + J...
متن کاملGroup Corings
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 comodu...
متن کاملWeak Corings
Entwined structures (A,C, ψ) were introduced by Brzeziński and Majid to study the interdependence of an R-algebra A and an R-coalgebra C, R a commutative ring. It turned out that this relationship can also be expressed by the fact that A⊗R C has a canonical A-coring structure. More generally weak entwined structures and their modules were studied by Caenepeel and Groot and it was suggested by C...
متن کاملOn Galois corings
For a long period the theory of modules over rings on the one hand and comodules and Hopf modules for coalgebras and bialgebras on the other side developed quite independently. In this talk we want to outline how ideas from module theory can be applied to enrich the theory of comodules and vice versa. For this we consider A-corings C with grouplike elements over a ring A, in particular Galois c...
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ژورنال
عنوان ژورنال: Algebras and Representation Theory
سال: 2009
ISSN: 1386-923X,1572-9079
DOI: 10.1007/s10468-009-9153-6