المؤلفون: Yuan, Qianqian, Yao, Hailou

مصطلحات موضوعية: keyword:quasi-finite silting comodule, keyword:finitely silting comodule, keyword:finitely tilting comodule, keyword:torsion pair, keyword:duality, msc:16T15, msc:18E40, msc:18G15

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Relation: mr:MR4632853; zbl:Zbl 07729533; 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

الاتاحة: http://hdl.handle.net/10338.dmlcz/151770

المؤلفون: Li, Yuan, Yao, Hailou

مصطلحات موضوعية: keyword:(pre)cover, keyword:tilting comodule, keyword:(co)localization, keyword:torsion theory, msc:16T15, msc:18E40, msc:18G05

وصف الملف: application/pdf

Relation: mr:MR4295238; zbl:07396190; reference:[1] Assem, I., Simson, D., Skowroński, A.: Elements of the Representation Theory of Associative Algebras. Volume 1. Techniques of Representation Theory.London Mathematical Society Student Texts 65. Cambridge University Press, Cambridge (2006). Zbl 1092.16001, MR 2197389, 10.1017/CBO9780511614309; reference:[2] Chin, W., Simson, D.: Coxeter transformation and inverses of Cartan matrices for coalgebras.J. Algebra 324 (2010), 2223-2248. Zbl 1214.16011, MR 2684139, 10.1016/j.jalgebra.2010.06.029; reference:[3] Cuadra, J., Gómez-Torrecillas, J.: Idempotents and Morita-Takeuchi theory.Commun. Algebra 30 (2002), 2405-2426. Zbl 1006.16050, MR 1904645, 10.1081/AGB-120003476; reference:[4] Dăscălescu, S., Năstăsescu, C., Raianu, Ş.: Hopf Algebras: An Introduction.Pure and Applied Mathematics, Marcel Dekker 235. Marcel Dekker, New York (2001). Zbl 0962.16026, MR 1786197, 10.1201/9781482270747; reference:[5] Fu, X., Hu, Y., Yao, H.: The resolution dimensions with respect to balanced pairs in the recollement of abelian categories.J. Korean Math. Soc. 56 (2019), 1031-1048. Zbl 07128259, MR 3978243, 10.4134/JKMS.j180577; reference:[6] Fu, X., Yao, H.: On Gorenstein coalgebras.Front. Math. China 11 (2016), 845-867. Zbl 1370.16028, MR 3531034, 10.1007/s11464-016-0562-7; reference:[7] Gabriel, P.: Des catégories abéliennes.Bull. Soc. Math. Fr. 90 (1962), 323-448 French. Zbl 0201.35602, MR 0232821, 10.24033/bsmf.1583; reference:[8] Gómez-Torrecillas, J., Năstăsescu, C., Torrecillas, B.: Localization in coalgebras: Applications to finiteness conditions.J. Algebra Appl. 2 (2007), 233-243. Zbl 1145.16020, MR 2316418, 10.1142/S0219498807002156; reference:[9] Jara, P., Merino, L. M., Llena, D., Ştefan, D.: Hereditary and formally smooth coalgebras.Algebr. Represent. Theory 8 (2005), 363-374. Zbl 1098.16014, MR 2176142, 10.1007/s00000-005-8110-3; reference:[10] Jara, P., Merino, L. M., Navarro, G.: Localization in tame and wild coalgebras.J. Pure Appl. Algebra 211 (2007), 342-359. Zbl 1124.16014, MR 2340452, 10.1016/j.jpaa.2007.01.009; reference:[11] Jara, P., Merino, L. M., Navarro, G., Ruiz, J. F.: Localization in coalgebras: Stable localizations and path coalgebras.Commun. Algebra 34 (2006), 2843-2856. Zbl 1118.16027, MR 2250572, 10.1080/00927870600637066; reference:[12] Kleiner, M., Reiten, I.: Abelian categories, almost split sequences, and comodules.Trans. Am. Math. Soc. 357 (2005), 3201-3214. Zbl 1068.18010, MR 2135742, 10.1090/S0002-9947-04-03571-8; reference:[13] Kosakowska, J., Simson, D.: Hereditary coalgebras and representations of species.J. Algebra 293 (2005), 457-505. Zbl 1116.16038, MR 2173711, 10.1016/j.jalgebra.2005.04.019; reference:[14] Lin, B. I.: Semiperfect coalgebras.J. Algebra 49 (1977), 357-373. Zbl 0369.16010, MR 0498663, 10.1016/0021-8693(77)90246-0; reference:[15] Liu, H., Zhang, S.: Equivalences induced by $n$-self-cotilting comodules.Adv. Pure Appl. Math. 2 (2011), 109-131. Zbl 1221.16025, MR 2769312, 10.1515/apam.2010.029; reference:[16] Montgomery, S.: Hopf Algebras and Their Actions on Rings.Regional Conference Series in Mathematics 82. American Mathematical Society, Providence (1993). Zbl 0793.16029, MR 1243637, 10.1090/cbms/082; reference:[17] Montgomery, S.: Indecomposable coalgebras, simple comodules, and pointed Hopf algebras.Proc. Am. Math. Soc. 123 (1995), 2343-2351. Zbl 0836.16024, MR 1257119, 10.1090/S0002-9939-1995-1257119-3; reference:[18] Năstăsescu, C., Torrecillas, B.: Torsion theories for coalgebras.J. Pure Appl. Algebra 97 (1994), 203-220. Zbl 0820.16026, MR 1312762, 10.1016/0022-4049(94)00009-3; reference:[19] Năstăsescu, C., Torrecillas, B.: Colocalization on Grothendieck categories with applications to coalgebras.J. Algebra 185 (1996), 108-124. Zbl 0863.18007, MR 1409977, 10.1006/jabr.1996.0315; reference:[20] Navarro, G.: Representation Theory of Coalgebras. Localization in Coalgebras: PhD Thesis.Universidad de Granada, Granada (2006).; reference:[21] Navarro, G.: Simple comodules and localization in coalgebras.New Techniques in Hopf Algebras and Graded Ring Theory Koninklijke Vlaamse Academie van Belgie voor Wetenschappen en Kunsten, Brussel (2007), 141-164. Zbl 1146.16021, MR 2395772; reference:[22] Navarro, G.: Some remarks on localization in coalgebras.Commun. Algebra 36 (2008), 3447-3466. Zbl 1157.16013, MR 2441125, 10.1080/00927870802107868; reference:[23] Nowak, S., Simson, D.: Locally Dynkin quivers and hereditary coalgebras whose left comodules are direct sums of finite dimensional comodules.Commun. Algebra 30 (2002), 455-476. Zbl 1005.16037, MR 1880685, 10.1081/AGB-120006503; reference:[24] Radford, D. E.: On the structure of pointed coalgebras.J. Algebra 77 (1982), 1-14. Zbl 0487.16011, MR 0665161, 10.1016/0021-8693(82)90274-5; reference:[25] Simson, 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:[26] Simson, D.: Path coalgebras of quivers with relations and a tame-wild dichotomy problem for coalgebras.Rings, Modules, Algebras, and Abelian Groups Lecture Notes in Pure and Applied Mathematics 236. Marcel Dekker, New York (2004), 465-492. Zbl 1072.16015, MR 2050733; reference:[27] Simson, D.: Irreducible morphisms, the Gabriel quiver and colocalisations for coalgebras.Int. J. Math. Math. Sci. 2006 (2006), Article ID 47146, 16 pages. Zbl 1171.16008, MR 2251741, 10.1155/IJMMS/2006/47146; reference:[28] Simson, D.: Hom-computable coalgebras, a composition factors matrix and an Euler bilinear form of an Euler coalgebra.J. Algebra 315 (2007), 42-75. Zbl 1131.16020, MR 2344333, 10.1016/j.jalgebra.2007.01.024; reference:[29] Simson, D.: Localising embeddings of comodule categories with applications to tame and Euler coalgebras.J. Algebra 312 (2007), 455-494. Zbl 1136.16036, MR 2320469, 10.1016/j.jalgebra.2006.11.043; reference:[30] 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:[31] Simson, D.: Representation-directed incidence coalgebras of intervally finite posets and the tame-wild dichotomy.Commun. Algebra 36 (2008), 2764-2784. Zbl 1191.16035, MR 2422517, 10.1080/00927870802068342; reference:[32] Simson, D.: Tame-wild dichotomy for coalgebras.J. Lond. Math. Soc., II. Ser. 78 (2008), 783-797. Zbl 1175.16029, MR 2456905, 10.1112/jlms/jdn047; reference:[33] Simson, D.: Incidence coalgebras of intervally finite posets, their integral quadratic forms and comodule categories.Colloq. Math. 115 (2009), 259-295. Zbl 1173.16009, MR 2491748, 10.4064/cm115-2-9; reference:[34] Simson, D.: Coalgebras of tame comodule type, comodule categories, and a tame-wild dichotomy problem.Representation of Algebras and Related Topics EMS Series of Congress Reports, European Mathematical Society, Zürich (2011), 561-660. Zbl 1301.16042, MR 2931905, 10.4171/101-1/12; reference:[35] Sweedler, M. E.: Hopf Algebras.Mathematics Lecture Note Series. W. A. Benjamin, New York (1969). Zbl 0194.32901, MR 0252485; reference:[36] 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:[37] Wang, M.: Tilting comodules over semi-perfect coalgebras.Algebra Colloq. 6 (1999), 461-472. Zbl 0945.16034, MR 1809680; reference:[38] Woodcock, D.: Some categorical remarks on the representation theory of coalgebras.Commun. Algebra 25 (1997), 2775-2794. Zbl 0883.18011, MR 1458729, 10.1080/00927879708826022; reference:[39] Zhang, S., Yao, H.: Some remarks on cotilting comodules.Front. Math. China 9 (2014), 699-714. Zbl 1326.16030, MR 3195842, 10.1007/s11464-014-0345-y

الاتاحة: http://hdl.handle.net/10338.dmlcz/149049