Abstract
In this article, we apply the localization techniques to right (*)-serial coalgebras and obtain some interesting results. In particular, we give a characterization of right (*)-serial coalgebras by means of its ‘local structure’, which is the localized right (*)-serial coalgebras, and we get a main result—the periodicity theorem.
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References
Abe E. Hopf Algebras. Cambridge: Cambridge University Press, 1977
Chin W, Montgomery S. Basic coalgebra. AMS/IP Studies in Advanced Math, 1997, 4: 41–47
Gabriel P. Des catégories abeliennes. Bull Soc Math France, 1962, 90: 323–448
Garulo G N. Representation Theory of Coalgebras. Localization in Coalgebras. Ph D Thesis. Granada: Universidad de Granada, 2006
Gómez-Torrecillas J, Navarro G. Serial coalgebras and their valued Gabriel quivers. J Algebra, 2008, 319: 5039–5059
Goodearl K R, Warfield R B. An Introduction to Noncommutative Noetherian Rings. London Math Soc Student Series 16. Cambridge: Cambridge University Press, 1989
Green J A. Locally finite representations. J Algebra, 1976, 41: 137–171
Guadra J, Gómez-Torrecillas J. Idempotents and Morita-Takeuchi theory. Comm Algebra, 2002, 30: 2405–2426
Guadra J, Gómez-Torrecillas J. Serial coalgebras. J Pure and Applied Algebra, 2004, 189: 89–107
Jara P, Merino L M, Navarro G, Ruíz J F. Localization in coalgebras, stable localizations and path coalgebras. Comm Algebra, 2006, 34: 2843–2856
Kosakowska J, Simson D. Hereditary coalgebras and representations of species. J Algebra, 2005, 293: 457–505
McConnell J C, Robson J C. Noncommutative Noetherian Rings. New York: John Wiley, 1987
Montgomery S. Hopf Algebras and Their Actions on Rings. MBS, No 82. Providence: Amer Math Soc, 1993
Năstăsescu C, Torrecillas B. Torsion theories for coalgebras. J Pure and Applied Algebra, 1994, 97: 203–220
Navarro G. Some remarks on localization in coalgebras. Comm Algebra (in press). ArXiv.math.RA/0608425, 2007
Popescu N. Abelian categories with applications to rings and modules. London Mathematical Society Monographs, No 3. London-New York: Academic Press, 1973
Radford D E. On the structure of pointed coalgebras. J Algebra, 1982, 77: 1–14
Simson D. Path coalgebras of quiver with relations and a tame-wild dichotomy problem for coalgebras. Lecture Notes in Pure and Applied Mathematics, 2005, 236: 465–492
Sweedler M E. Hopf Algebras. New York: Benjamin, 1969
Takeuchi M. Morita theorems for categories of comodules. J Fac Sci Uni Tokyo, 1977, 24: 629–644
Woodcock D. Some categorical remarks on the representation theory of coalgebras. Comm Algebra, 1997, 25: 2775–2794
Yao Hailou, Fan Weili. Finite dimensional (*)-serial algebras. Sci China Ser A (to appear)
Yao Hailou, Fan Weili. (*)-Serial coalgebras. Preprint, 2010
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Fan, W., Yao, H. Localization in right (*)-serial coalgebras. Front. Math. China 5, 635–652 (2010). https://doi.org/10.1007/s11464-010-0077-6
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DOI: https://doi.org/10.1007/s11464-010-0077-6