| Title:
|
Strict Mittag-Leffler conditions and locally split morphisms (English) |
| Author:
|
Yang, Yanjiong |
| Author:
|
Yan, Xiaoguang |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
68 |
| Issue:
|
3 |
| Year:
|
2018 |
| Pages:
|
677-686 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
strict Mittag-Leffler condition |
| Keyword:
|
locally split morphism |
| Keyword:
|
Gorenstein projective module |
| Keyword:
|
Ding projective module |
| MSC:
|
13D02 |
| MSC:
|
13D07 |
| MSC:
|
13E05 |
| MSC:
|
16D10 |
| MSC:
|
16D80 |
| MSC:
|
16D90 |
| idZBL:
|
Zbl 06986965 |
| idMR:
|
MR3851884 |
| DOI:
|
10.21136/CMJ.2018.0621-16 |
| . |
| Date available:
|
2018-08-09T13:11:13Z |
| Last updated:
|
2020-10-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147361 |
| . |
| Reference:
|
[1] Hügel, L. Angeleri, Bazzoni, S., Herbera, D.: A solution to the Baer splitting problem.Trans. Am. Math. Soc. 360 (2008), 2409-2421. Zbl 1136.13005, MR 2373319, 10.1090/S0002-9947-07-04255-9 |
| Reference:
|
[2] Hügel, L. Angeleri, Herbera, D.: Mittag-Leffler conditions on modules.Indiana Univ. Math. J. 57 (2008), 2459-2517. Zbl 1206.16002, MR 2463975, 10.1512/iumj.2008.57.3325 |
| Reference:
|
[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. Zbl 0743.16003, MR 1144024, 10.1090/conm/124 |
| Reference:
|
[4] Bazzoni, S., Herbera, D.: One dimensional tilting modules are of finite type.Algebr. Represent. Theory 11 (2008), 43-61. Zbl 1187.16008, MR 2369100, 10.1007/s10468-007-9064-3 |
| Reference:
|
[5] Bazzoni, S., Šťovíček, J.: All tilting modules are of finite type.Proc. Am. Math. Soc. 135 (2007), 3771-3781. Zbl 1132.16008, MR 2341926, 10.1090/S0002-9939-07-08911-3 |
| Reference:
|
[6] Bennis, D., Mahdou, N.: Strongly Gorenstein projective, injective, and flat modules.J. Pure Appl. Algebra 210 (2007), 437-445. Zbl 1118.13014, MR 2320007, 10.1016/j.jpaa.2006.10.010 |
| Reference:
|
[7] Chase, S. U.: Direct products of modules.Trans. Am. Math. Soc. 97 (1960), 457-473. Zbl 0100.26602, MR 0120260, 10.2307/1993382 |
| Reference:
|
[8] Ding, N., Li, Y., Mao, L.: Strongly Gorenstein flat modules.J. Aust. Math. Soc. 86 (2009), 323-338. Zbl 1200.16010, MR 2529328, 10.1017/S1446788708000761 |
| Reference:
|
[9] Emmanouil, I.: On certain cohomological invariants of groups.Adv. Math. 225 (2010), 3446-3462. Zbl 1214.20050, MR 2729012, 10.1016/j.aim.2010.06.007 |
| Reference:
|
[10] Emmanouil, I., Talelli, O.: On the flat length of injective modules.J. Lond. Math. Soc., II. Ser. 84 (2011), 408-432. Zbl 1237.16004, MR 2835337, 10.1112/jlms/jdr014 |
| Reference:
|
[11] Enochs, E. E., Jenda, O. M. G.: Relative Homological Algebra.De Gruyter Expositions in Mathematics 30, Walter de Gruyter, Berlin (2000). Zbl 0952.13001, MR 1753146, 10.1515/9783110803662 |
| Reference:
|
[12] Gillespie, J.: Model structures on modules over Ding-Chen rings.Homology Homotopy Appl. 12 (2010), 61-73. Zbl 1231.16005, MR 2607410, 10.4310/HHA.2010.v12.n1.a6 |
| Reference:
|
[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. Zbl 0235.14007, MR 1611786 |
| Reference:
|
[14] Herbera, D., Trlifaj, J.: Almost free modules and Mittag-Leffler conditions.Adv. Math. 229 (2012), 3436-3467. Zbl 1279.16001, MR 2900444, 10.1016/j.aim.2012.02.013 |
| Reference:
|
[15] Raynaud, M., Gruson, L.: Critères de platitude et de projectivité. Techniques de ``platification'' d'un module.Invent. Math. 13 (1971), 1-89 French. Zbl 0227.14010, MR 0308104, 10.1007/BF01390094 |
| Reference:
|
[16] Zimmermann, W.: On locally pure-injective modules.J. Pure Appl. Algebra 166 (2002), 337-357. Zbl 0993.16002, MR 1870625, 10.1016/S0022-4049(01)00011-1 |
| . |
