Some remarks on cotilting comodules

doi:10.1007/s11464-014-0345-y

Front. Math. China

2014, Vol. 9

Issue (3) : 699-714 https://doi.org/10.1007/s11464-014-0345-y

RESEARCH ARTICLE

Some remarks on cotilting comodules

Sujuan ZHANG^1,²,Hailou YAO^1,^*(

)

1. College of Applied Sciences, Beijing University of Technology, Beijing 100124, China
2. Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China

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Abstract

We study cotilting comodules and f-cotilting comodules and give a description of localization of f-cotilting comodules and classical tilting comodules. First, we introduce T-cotilting injective comodules and their dimensions which are important for researching cotilting comodules. Then we characterize the localization in f-cotilting comodules, finitely copresented comodules, and classical tilting comodules. In particular, we obtain a localizing property about finitely copresented comodules.

Keywords Coalgebra comodule localization

Corresponding Author(s): Hailou YAO

Issue Date: 24 June 2014

Cite this article:

Sujuan ZHANG,Hailou YAO. Some remarks on cotilting comodules[J]. Front. Math. China, 2014, 9(3): 699-714.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-014-0345-y
https://academic.hep.com.cn/fmc/EN/Y2014/V9/I3/699

1	GabrielP. Des categories abeliennes. Bull Soc Math France, 1962, 90: 323-448
2	GöbelR, PrelleR. Solution of two problems on cotorsion Abelian groups, Arch Math, 1978, 31: 423-431 doi: 10.1007/BF01226469
3	GoodearlK R. Localization and splitting in hereditary noetherian prime rings. Pacific J Math, 1974, 53(1): 137-151 doi: 10.2140/pjm.1974.53.137
4	GoodearlK R, WarfieldR B. An Introduction to Noncommutative Noetherian Rings. London Math Soc Student Ser 16. Cambridge: Cambridge Univ Press, 1989
5	JaraP, MerinoL M, NavarroG. On path coalgebras of quivers with relations. Colloq Math, 2005, 102: 49-65 doi: 10.4064/cm102-1-5
6	JaraP, MerinoL M, NavarroG. Localization in tame and wild coalgebras. J Pure Appl Algebra, 2007, 211: 342-359 doi: 10.1016/j.jpaa.2007.01.009
7	JaraP, MerinoL M, NavarroG, RuizJ F. Localization in coalgebras. Stable localizations and path coalgebras. Comm Algebra, 2006, 34: 2843-2856 doi: 10.1080/00927870600637066
8	NăstăsescuC, TorrecillasB. Colocalization on Grothendieck categories with applications to coalgebras. J Algebra, 1996, 185: 108-124 doi: 10.1006/jabr.1996.0315
9	NavarroG. Representation Theory of Coalgebras. Localization in Coalgebras Ph D Thesis. Granada: Universidad de Granada, 2006
10	NavarroG. Some remarks on localization in coalgebras. Comm Algebra, 2008, 36: 3447-3466 doi: 10.1080/00927870802107868
11	SimsonD. Cotilted coalgebras and tame comodule type. Arab J Sci Eng, 2008, 33: 421-445
12	WangM. Tilting comodules over semi-perfect coalgebras. Algebra Colloq, 1999, 6: 461-472
13	WoodcockD. Some categorical remarks on the representation theory of coalgebras. Comm Algebra, 1997, 25(9): 2775-2794 doi: 10.1080/00927879708826022

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