Some remarks on cotilting comodules

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

References

[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

[3] GoodearlK R. Localization and splitting in hereditary noetherian prime rings. Pacific J Math, 1974, 53(1): 137-151

[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

[6] JaraP, MerinoL M, NavarroG. Localization in tame and wild coalgebras. J Pure Appl Algebra, 2007, 211: 342-359

[7] JaraP, MerinoL M, NavarroG, RuizJ F. Localization in coalgebras. Stable localizations and path coalgebras. Comm Algebra, 2006, 34: 2843-2856

[8] NăstăsescuC, TorrecillasB. Colocalization on Grothendieck categories with applications to coalgebras. J Algebra, 1996, 185: 108-124

[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

[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

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg