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Strict Mittag-Leffler conditions and locally split morphisms
Czechoslovak Mathematical Journal, Tome 68 (2018) no. 3, pp. 677-686 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper, we prove that any pure submodule of a strict Mittag-Leffler module is a locally split submodule. As applications, we discuss some relations between locally split monomorphisms and locally split epimorphisms and give a partial answer to the open problem whether Gorenstein projective modules are Ding projective.
In this paper, we prove that any pure submodule of a strict Mittag-Leffler module is a locally split submodule. As applications, we discuss some relations between locally split monomorphisms and locally split epimorphisms and give a partial answer to the open problem whether Gorenstein projective modules are Ding projective.
DOI : 10.21136/CMJ.2018.0621-16
Classification : 13D02, 13D07, 13E05, 16D10, 16D80, 16D90
Keywords: strict Mittag-Leffler condition; locally split morphism; Gorenstein projective module; Ding projective module 
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Yang, Yanjiong; Yan, Xiaoguang. Strict Mittag-Leffler conditions and locally split morphisms. Czechoslovak Mathematical Journal, Tome 68 (2018) no. 3, pp. 677-686. doi: 10.21136/CMJ.2018.0621-16

[1] Hügel, L. Angeleri, Bazzoni, S., Herbera, D.: A solution to the Baer splitting problem. Trans. Am. Math. Soc. 360 (2008), 2409-2421. | DOI | MR | JFM

[2] Hügel, L. Angeleri, Herbera, D.: Mittag-Leffler conditions on modules. Indiana Univ. Math. J. 57 (2008), 2459-2517. | DOI | MR | JFM

[3] Azumaya, G.: Locally pure-projective modules. Azumaya Algebras, Actions, and Modules Proc. Conf., Bloomington 1990, Contemp. Math. 124, Am. Math. Soc., Providence (1992), 17-22. | DOI | MR | JFM

[4] Bazzoni, S., Herbera, D.: One dimensional tilting modules are of finite type. Algebr. Represent. Theory 11 (2008), 43-61. | DOI | MR | JFM

[5] Bazzoni, S., Šťovíček, J.: All tilting modules are of finite type. Proc. Am. Math. Soc. 135 (2007), 3771-3781. | DOI | MR | JFM

[6] Bennis, D., Mahdou, N.: Strongly Gorenstein projective, injective, and flat modules. J. Pure Appl. Algebra 210 (2007), 437-445. | DOI | MR | JFM

[7] Chase, S. U.: Direct products of modules. Trans. Am. Math. Soc. 97 (1960), 457-473. | DOI | MR | JFM

[8] Ding, N., Li, Y., Mao, L.: Strongly Gorenstein flat modules. J. Aust. Math. Soc. 86 (2009), 323-338. | DOI | MR | JFM

[9] Emmanouil, I.: On certain cohomological invariants of groups. Adv. Math. 225 (2010), 3446-3462. | DOI | MR | JFM

[10] Emmanouil, I., Talelli, O.: On the flat length of injective modules. J. Lond. Math. Soc., II. Ser. 84 (2011), 408-432. | DOI | MR | JFM

[11] Enochs, E. E., Jenda, O. M. G.: Relative Homological Algebra. De Gruyter Expositions in Mathematics 30, Walter de Gruyter, Berlin (2000). | DOI | MR | JFM

[12] Gillespie, J.: Model structures on modules over Ding-Chen rings. Homology Homotopy Appl. 12 (2010), 61-73. | DOI | MR | JFM

[13] Grothendieck, A.: Techniques de construction et théorèmes d'existence en géométrie algébrique. III. Préschemas quotients. Sém. Bourbaki, Vol. 6, 1960-1961 Soc. Math. France, Paris (1995), French 99-118. | MR | JFM

[14] Herbera, D., Trlifaj, J.: Almost free modules and Mittag-Leffler conditions. Adv. Math. 229 (2012), 3436-3467. | DOI | MR | JFM

[15] Raynaud, M., Gruson, L.: Critères de platitude et de projectivité. Techniques de ``platification'' d'un module. Invent. Math. 13 (1971), 1-89 French. | DOI | MR | JFM

[16] Zimmermann, W.: On locally pure-injective modules. J. Pure Appl. Algebra 166 (2002), 337-357. | DOI | MR | JFM

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