کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4598207 1336268 2007 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Chain and distributive coalgebras
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Chain and distributive coalgebras
چکیده انگلیسی
We show that coalgebras whose lattice of right coideals is distributive are coproducts of coalgebras whose lattice of right coideals is a chain. Those chain coalgebras are characterized as finite duals of Noetherian chain rings whose residue field is a finite dimensional division algebra over the base field. They also turn out to be coreflexive. Infinite dimensional chain coalgebras are finite duals of left Noetherian chain domains. Given any finite dimensional division algebra D and D-bimodule structure on D, we construct a chain coalgebra as a cotensor coalgebra. Moreover if D is separable over the base field, every chain coalgebra of type D can be embedded in such a cotensor coalgebra. As a consequence, cotensor coalgebras arising in this way are the only infinite dimensional chain coalgebras over perfect fields. Finite duals of power series rings with coeficients in a finite dimensional division algebra D are further examples of chain coalgebras, which also can be seen as tensor products of D∗, and the divided power coalgebra and can be realized as the generalized path coalgebra of a loop. If D is central, any chain coalgebra is a subcoalgebra of the finite dual of D[[x]].
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Pure and Applied Algebra - Volume 211, Issue 3, December 2007, Pages 581-595
نویسندگان
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