Frontiers of Mathematics in China >
Some remarks on cotilting comodules
Received date: 21 Jun 2013
Accepted date: 06 Nov 2013
Published date: 24 Jun 2014
Copyright
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.
Key words: Coalgebra; comodule; localization
Sujuan ZHANG , Hailou YAO . Some remarks on cotilting comodules[J]. Frontiers of Mathematics in China, 2014 , 9(3) : 699 -714 . DOI: 10.1007/s11464-014-0345-y
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
|
/
〈 | 〉 |