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Title: Finitely silting comodules in quasi-finite comodule category (English)
Author: Yuan, Qianqian
Author: Yao, Hailou
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 73
Issue: 3
Year: 2023
Pages: 695-714
Summary lang: English
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Category: math
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Summary: 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. (English)
Keyword: quasi-finite silting comodule
Keyword: finitely silting comodule
Keyword: finitely tilting comodule
Keyword: torsion pair
Keyword: duality
MSC: 16T15
MSC: 18E40
MSC: 18G15
idZBL: Zbl 07729533
idMR: MR4632853
DOI: 10.21136/CMJ.2023.0173-22
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Date available: 2023-08-11T14:20:59Z
Last updated: 2023-09-13
Stable URL: http://hdl.handle.net/10338.dmlcz/151770
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Reference: [1] Adachi, T., Iyama, O., Reiten, I.: $\tau$-tilting theory.Compos. Math. 150 (2014), 415-452. Zbl 1330.16004, MR 3187626, 10.1112/S0010437X13007422
Reference: [2] Takhman, K. Al: Equivalences of comodule categories for coalgebras over rings.J. Pure Appl. Algebra 173 (2002), 245-271. Zbl 1004.16039, MR 1916479, 10.1016/S0022-4049(02)00013-0
Reference: [3] Anderson, F. W., Fuller, K. R.: Rings and Categories of Modules.Graduate Texts in Mathematics 13. Springer, New York (1974). Zbl 0301.16001, MR 0417223, 10.1007/978-1-4612-4418-9
Reference: [4] Hügel, L. Angeleri, Hrbek, M.: Silting modules over commutative rings.Int. Math. Res. Not. 2017 (2017), 4131-4151. Zbl 1405.13018, MR 3671512, 10.1093/imrn/rnw147
Reference: [5] Hügel, L. Angeleri, Marks, F., Vitória, J.: Silting modules.Int. Math. Res. Not. 2016 (2016), 1251-1284. Zbl 1367.16005, MR 3493448, 10.1093/imrn/rnv191
Reference: [6] Colby, R. R., Fuller, K. R.: Equivalence and Duality for Module Categories: With Tilting and Cotilting for Rings.Cambridge Tracts in Mathematics 161. Cambridge University Press, Cambridge (2004). Zbl 1069.16001, MR 2048277, 10.1017/CBO9780511546518
Reference: [7] Colpi, R., Trlifaj, J.: Tilting modules and tilting torsion theories.J. Algebra 178 (1995), 614-634. Zbl 0849.16033, MR 1359905, 10.1006/jabr.1995.1368
Reference: [8] Doi, Y.: Homological coalgebra.J. Math. Soc. Japan 33 (1981), 31-50. Zbl 0459.16007, MR 0597479, 10.2969/jmsj/03310031
Reference: [9] Keller, B., Vossieck, D.: Aisles in derived categories.Bull. Soc. Math. Belg., Sér. A 40 (1988), 239-253. Zbl 0671.18003, MR 0976638
Reference: [10] Krause, H., Saorín, M.: On minimal approximations of modules.Trends in the Representation Theory of Finite Dimensional Algebras Contemporary Mathematics 229. AMS, Providence (1998), 227-236. Zbl 0959.16003, MR 1676223, 10.1090/conm/229
Reference: [11] Lin, B. I.: Semiperfect coalgebras.J. Algebra 49 (1977), 357-373. Zbl 0369.16010, MR 0498663, 10.1016/0021-8693(77)90246-0
Reference: [12] Positselski, L.: Dedualizing complexes of bicomodules and MGM duality over coalgebras.Algebr. Represent. Theory 21 (2018), 737-767. Zbl 1394.16040, MR 3826725, 10.1007/s10468-017-9736-6
Reference: [13] Simsom, D.: Coalgebras, comodules, pseudocompact algebras and tame comodule type.Colloq. Math. 90 (2001), 101-150. Zbl 1055.16038, MR 1874368, 10.4064/cm90-1-9
Reference: [14] Simson, D.: Cotilted coalgebras and tame comodule type.Arab. J. Sci. Eng., Sect. C, Theme Issues 33 (2008), 421-445. Zbl 1186.16039, MR 2500051
Reference: [15] Takeuchi, M.: Morita theorems for categories of comodules.J. Fac. Sci., Univ. Tokyo, Sect. I A 24 (1977), 629-644. Zbl 0385.18007, MR 0472967
Reference: [16] Wang, M.-Y.: Some co-hom functors and classical tilting comodules.Southeast Asian Bull. Math. 22 (1998), 455-468. Zbl 0942.16047, MR 1811188
Reference: [17] Wang, M.: Tilting comodules over semi-perfect coalgebras.Algebra Colloq. 6 (1999), 461-472. Zbl 0945.16034, MR 1809680
Reference: [18] Wang, M.: Morita Equivalence and Its Generalizations.Science Press, Beijing (2001).
Reference: [19] Yuan, Q. Q., Yao, H.-L.: On silting comodules.J. Shandong. Univ. 57 (2022), 1-7. 10.6040/j.issn.1671-9352.0.2021.503
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