JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (8): 1-5.doi: 10.6040/j.issn.1671-9352.0.2019.869

   

On torsion free class and cover class in category of comodules

LI Yuan, YAO Hai-lou*   

  1. College of Applied Sciences, Beijing University of Technology, Beijing 100124, China
  • Published:2020-07-14

Abstract: For a coalgebra, the concept of(pre)covers for comodules is first introduced and some properties about them are given. Then, the concepts of maximal tilting comodules and cover comodules are given, and the existence of a bijection between the tilting torsion free classes and the maximal tilting comodules is proved. Finally, when the tilting torsion free class is a cover class, whose unique representation by cover comodules over a coalgebra is obtained.

Key words: cover class, maximal tilting, torsion free class, cover comodule

CLC Number: 

  • O153.3
[1] BRENNER S, BUTLER M. Generalnizations of the Bernstein-Gelfand-Ponomarev reflections fuctors[M] // Representation Theory Ⅱ. Lecture Notes in Mathematics, Vol. 832. Berlin: Springer, 1980: 103-169.
[2] HAPPEL D, RINGEL C M. Tilted algebras[J]. Trans Amer Math Soc, 1982, 274:399-443.
[3] COLPI R, TONOLO A, TRLIFAJ J. Partial cotilting modules and the lattices induced by them[J]. Comm Algebra, 1997, 25(10):3225-3237.
[4] HÜGEL L. Tilting preenvelopes and cotilting precovers[J]. Algebras and Representation Theory, 2001, 4:155-170.
[5] DOI Y. Homological coalgebra[J]. J Math Soc Japan, 1981, 33(1):31-50.
[6] SIMSON D. Hom-computable coalgebras, a composition factors matrix and an Euler bilinear form of an Euler coalgebra[J]. J Algebra, 2007, 315(1):42-75.
[7] SIMSON D. Cotilted coalgebras and tame comodule type[J]. Arab J Sci Eng, 2008, 33(2):421-445.
[8] SIMSON D. Coalgebras, comodules, pseudocompact algebras and tame comodule comodule type[J]. Colloq Math, 2001, 90(1):101-150.
[9] CHIN W, SIMSON D. Coxeter transformation and inverses of Cartan matrices for coalgebras[J]. J Algebra, 2010, 324(9):2223-2248.
[10] CHIN W. A brief introduction to coalgebra representation theory[J]. Lect Notes Pure Appl Math, 2004, 237:109-131.
[11] LIN B I-P. Semiperfect coalgebras[J]. J Algebra, 1977, 49(2):357-373.
[12] WANG M Y. Tilting comodules over semi-perfect coalgebras[J]. Algebra Colloq, 1999, 6(4):461-472.
[1] FENG Xiao and ZHANG Shun-hua . τ-Flat test modules and τ-flatcover [J]. J4, 2007, 42(1): 31-34 .
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!