Finitely silting comodules in quasi-finite comodule category

Qianqian Yuan; Hailou Yao

Czechoslovak Mathematical Journal (2023)

  • Volume: 73, Issue: 3, page 695-714
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Yuan, Qianqian, and Yao, Hailou. "Finitely silting comodules in quasi-finite comodule category." Czechoslovak Mathematical Journal 73.3 (2023): 695-714. <http://eudml.org/doc/299097>.

@article{Yuan2023,
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.},
author = {Yuan, Qianqian, Yao, Hailou},
journal = {Czechoslovak Mathematical Journal},
keywords = {quasi-finite silting comodule; finitely silting comodule; finitely tilting comodule; torsion pair; duality},
language = {eng},
number = {3},
pages = {695-714},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Finitely silting comodules in quasi-finite comodule category},
url = {http://eudml.org/doc/299097},
volume = {73},
year = {2023},
}

TY - JOUR
AU - Yuan, Qianqian
AU - Yao, Hailou
TI - Finitely silting comodules in quasi-finite comodule category
JO - Czechoslovak Mathematical Journal
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 73
IS - 3
SP - 695
EP - 714
AB - 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.
LA - eng
KW - quasi-finite silting comodule; finitely silting comodule; finitely tilting comodule; torsion pair; duality
UR - http://eudml.org/doc/299097
ER -

References

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  1. Adachi, T., Iyama, O., Reiten, I., 10.1112/S0010437X13007422, Compos. Math. 150 (2014), 415-452. (2014) Zbl1330.16004MR3187626DOI10.1112/S0010437X13007422
  2. Takhman, K. Al, 10.1016/S0022-4049(02)00013-0, J. Pure Appl. Algebra 173 (2002), 245-271. (2002) Zbl1004.16039MR1916479DOI10.1016/S0022-4049(02)00013-0
  3. Anderson, F. W., Fuller, K. R., 10.1007/978-1-4612-4418-9, Graduate Texts in Mathematics 13. Springer, New York (1974). (1974) Zbl0301.16001MR0417223DOI10.1007/978-1-4612-4418-9
  4. Hügel, L. Angeleri, Hrbek, M., 10.1093/imrn/rnw147, Int. Math. Res. Not. 2017 (2017), 4131-4151. (2017) Zbl1405.13018MR3671512DOI10.1093/imrn/rnw147
  5. Hügel, L. Angeleri, Marks, F., Vitória, J., 10.1093/imrn/rnv191, Int. Math. Res. Not. 2016 (2016), 1251-1284. (2016) Zbl1367.16005MR3493448DOI10.1093/imrn/rnv191
  6. Colby, R. R., Fuller, K. R., 10.1017/CBO9780511546518, Cambridge Tracts in Mathematics 161. Cambridge University Press, Cambridge (2004). (2004) Zbl1069.16001MR2048277DOI10.1017/CBO9780511546518
  7. Colpi, R., Trlifaj, J., 10.1006/jabr.1995.1368, J. Algebra 178 (1995), 614-634. (1995) Zbl0849.16033MR1359905DOI10.1006/jabr.1995.1368
  8. Doi, Y., 10.2969/jmsj/03310031, J. Math. Soc. Japan 33 (1981), 31-50. (1981) Zbl0459.16007MR0597479DOI10.2969/jmsj/03310031
  9. Keller, B., Vossieck, D., Aisles in derived categories, Bull. Soc. Math. Belg., Sér. A 40 (1988), 239-253. (1988) Zbl0671.18003MR0976638
  10. Krause, H., Saorín, M., 10.1090/conm/229, Trends in the Representation Theory of Finite Dimensional Algebras Contemporary Mathematics 229. AMS, Providence (1998), 227-236. (1998) Zbl0959.16003MR1676223DOI10.1090/conm/229
  11. Lin, B. I., 10.1016/0021-8693(77)90246-0, J. Algebra 49 (1977), 357-373. (1977) Zbl0369.16010MR0498663DOI10.1016/0021-8693(77)90246-0
  12. Positselski, L., 10.1007/s10468-017-9736-6, Algebr. Represent. Theory 21 (2018), 737-767. (2018) Zbl1394.16040MR3826725DOI10.1007/s10468-017-9736-6
  13. Simsom, D., 10.4064/cm90-1-9, Colloq. Math. 90 (2001), 101-150. (2001) Zbl1055.16038MR1874368DOI10.4064/cm90-1-9
  14. Simson, D., Cotilted coalgebras and tame comodule type, Arab. J. Sci. Eng., Sect. C, Theme Issues 33 (2008), 421-445. (2008) Zbl1186.16039MR2500051
  15. Takeuchi, M., Morita theorems for categories of comodules, J. Fac. Sci., Univ. Tokyo, Sect. I A 24 (1977), 629-644. (1977) Zbl0385.18007MR0472967
  16. Wang, M.-Y., Some co-hom functors and classical tilting comodules, Southeast Asian Bull. Math. 22 (1998), 455-468. (1998) Zbl0942.16047MR1811188
  17. Wang, M., Tilting comodules over semi-perfect coalgebras, Algebra Colloq. 6 (1999), 461-472. (1999) Zbl0945.16034MR1809680
  18. Wang, M., Morita Equivalence and Its Generalizations, Science Press, Beijing (2001). (2001) 
  19. Yuan, Q. Q., Yao, H.-L., 10.6040/j.issn.1671-9352.0.2021.503, J. Shandong. Univ. 57 (2022), 1-7. (2022) DOI10.6040/j.issn.1671-9352.0.2021.503

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