کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9493138 | 1630564 | 2005 | 35 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Galois comodules
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Galois comodules Galois comodules](/preview/png/9493138.png)
چکیده انگلیسی
Galois comodules of a coring are studied. The conditions for a simple comodule to be a Galois comodule are found. A special class of Galois comodules termed principal comodules is introduced. These are defined as Galois comodules that are projective over their comodule endomorphism rings. A complete description of principal comodules in the case a background ring is a field is found. In particular it is shown that a (finitely generated and projective) right comodule of an A-coring C is principal provided a lifting of the canonical map is a split epimorphism in the category of left C-comodules. This description is then used to characterise principal extensions or non-commutative principal bundles. Specifically, it is proven that, over a field, any entwining structure consisting of an algebra A, a coseparable coalgebra C and a bijective entwining map Ï together with a group-like element in C give rise to a principal extension, provided the lifted canonical map is surjective. Induction of Galois and principal comodules via morphisms of corings is described. A connection between the relative injectivity of a Galois comodule and the properties of the extension of endomorphism rings associated to this comodule is revealed.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 290, Issue 2, 15 August 2005, Pages 503-537
Journal: Journal of Algebra - Volume 290, Issue 2, 15 August 2005, Pages 503-537
نویسندگان
Tomasz BrzeziÅski,