Skip to main content
SpringerLink
Log in

Finitely silting comodules in quasi-finite comodule category

  • Published:
Czechoslovak Mathematical Journal Aims and scope Submit manuscript

Abstract

We introduce the notions of silting comodules and finitely silting comodules in quasi-finite category, and study some properties of them. We investigate the torsion pair and dualities which are related to finitely silting comodules, and give the equivalences among silting comodules, finitely silting comodules, tilting comodules and finitely tilting comodules.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. T. Adachi, O. Iyama, I. Reiten: τ-tilting theory. Compos. Math. 150 (2014), 415–452.

    Article  MathSciNet  MATH  Google Scholar 

  2. K. Al Takhman: Equivalences of comodule categories for coalgebras over rings. J. Pure Appl. Algebra 173 (2002), 245–271.

    Article  MathSciNet  MATH  Google Scholar 

  3. F. W. Anderson, K. R. Fuller: Rings and Categories of Modules. Graduate Texts in Mathematics 13. Springer, New York, 1974.

    Google Scholar 

  4. L. Angeleri Hügel, M. Hrbek: Silting modules over commutative rings. Int. Math. Res. Not. 2017 (2017), 4131–4151.

    MathSciNet  MATH  Google Scholar 

  5. L. Angeleri Hiigel, F. Marks, J. Vitória: Silting modules. Int. Math. Res. Not. 2016 (2016), 1251–1284.

    Article  MathSciNet  MATH  Google Scholar 

  6. R. R. Colby, K. R. Fuller: Equivalence and Duality for Module Categories: With Tilting and Cotilting for Rings. Cambridge Tracts in Mathematics 161. Cambridge University Press, Cambridge, 2004.

    Google Scholar 

  7. R. Colpi, J. Trlifaj: Tilting modules and tilting torsion theories. J. Algebra 178 (1995), 614–634.

    Article  MathSciNet  MATH  Google Scholar 

  8. Y. Doi: Homological coalgebra. J. Math. Soc. Japan 33 (1981), 31–50.

    Article  MathSciNet  MATH  Google Scholar 

  9. B. Keller, D. Vossieck: Aisles in derived categories. Bull. Soc. Math. Belg., Sér. A 40 (1988), 239–253.

    MathSciNet  MATH  Google Scholar 

  10. H. Krause, M. Saorín: On minimal approximations of modules. Trends in the Representation Theory of Finite Dimensional Algebras. Contemporary Mathematics 229. AMS, Providence, 1998, pp. 227–236.

    Chapter  MATH  Google Scholar 

  11. B. I. Lin: Semiperfect coalgebras. J. Algebra 49 (1977), 357–373.

    Article  MathSciNet  MATH  Google Scholar 

  12. L. Positselski: Dedualizing complexes of bicomodules and MGM duality over coalgebras. Algebr. Represent. Theory 21 (2018), 737–767.

    Article  MathSciNet  MATH  Google Scholar 

  13. D. Simsom: Coalgebras, comodules, pseudocompact algebras and tame comodule type. Colloq. Math. 90 (2001), 101–150.

    Article  MathSciNet  MATH  Google Scholar 

  14. D. Simson: Cotilted coalgebras and tame comodule type. Arab. J. Sci. Eng., Sect. C, Theme Issues 33 (2008), 421–445.

    MathSciNet  MATH  Google Scholar 

  15. M. Takeuchi: Morita theorems for categories of comodules. J. Fac. Sci., Univ. Tokyo, Sect. I A 24 (1977), 629–644.

    MathSciNet  MATH  Google Scholar 

  16. M.-Y. Wang: Some co-hom functors and classical tilting comodules. Southeast Asian Bull. Math. 22 (1998), 455–468.

    MathSciNet  MATH  Google Scholar 

  17. M. Wang: Tilting comodules over semi-perfect coalgebras. Algebra Colloq. 6 (1999), 461–472.

    MathSciNet  MATH  Google Scholar 

  18. M. Wang: Morita Equivalence and Its Generalizations. Science Press, Beijing, 2001.

    Google Scholar 

  19. Q. Q. Yuan, H.-L. Yao: On silting comodules. J. Shandong. Univ. 57 (2022), 1–7.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Beijing University of Technology, Beijing, 100124, P. R. China

    Qianqian Yuan & Hailou Yao

Authors
  1. Qianqian Yuan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hailou Yao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hailou Yao.

Additional information

This work was supported by the National Science Foundation of China (Grant No. 12071120).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yuan, Q., Yao, H. Finitely silting comodules in quasi-finite comodule category. Czech Math J 73, 695–714 (2023). https://doi.org/10.21136/CMJ.2023.0173-22

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.21136/CMJ.2023.0173-22

Keywords

MSC 2020

Search

Navigation