کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4667912 1345486 2007 38 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Morita theory for coring extensions and cleft bicomodules
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Morita theory for coring extensions and cleft bicomodules
چکیده انگلیسی

A Morita context is constructed for any comodule of a coring and, more generally, for an L-C bicomodule Σ for a coring extension (D:L) of (C:A). It is related to a 2-object subcategory of the category of k-linear functors MC→MD. Strictness of the Morita context is shown to imply the Galois property of Σ as a C-comodule and a Weak Structure Theorem. Sufficient conditions are found also for a Strong Structure Theorem to hold.Cleft property of an L-C bicomodule Σ—implying strictness of the associated Morita context—is introduced. It is shown to be equivalent to being a GaloisC-comodule and isomorphic to EndC(Σ)⊗LD, in the category of left modules for the ring EndC(Σ) and right comodules for the coring D, i.e. satisfying the normal basis property.Algebra extensions, that are cleft extensions by a Hopf algebra, a coalgebra or a Hopf algebroid, as well as cleft entwining structures (over commutative or non-commutative base rings) and cleft weak entwining structures, are shown to provide examples of cleft bicomodules.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 209, Issue 2, 1 March 2007, Pages 611-648