Strict Mittag-Leffler conditions and locally split morphisms

Yanjiong Yang; Xiaoguang Yan

Czechoslovak Mathematical Journal (2018)

  • Volume: 68, Issue: 3, page 677-686
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Yang, Yanjiong, and Yan, Xiaoguang. "Strict Mittag-Leffler conditions and locally split morphisms." Czechoslovak Mathematical Journal 68.3 (2018): 677-686. <http://eudml.org/doc/294739>.

@article{Yang2018,
abstract = {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.},
author = {Yang, Yanjiong, Yan, Xiaoguang},
journal = {Czechoslovak Mathematical Journal},
keywords = {strict Mittag-Leffler condition; locally split morphism; Gorenstein projective module; Ding projective module},
language = {eng},
number = {3},
pages = {677-686},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Strict Mittag-Leffler conditions and locally split morphisms},
url = {http://eudml.org/doc/294739},
volume = {68},
year = {2018},
}

TY - JOUR
AU - Yang, Yanjiong
AU - Yan, Xiaoguang
TI - Strict Mittag-Leffler conditions and locally split morphisms
JO - Czechoslovak Mathematical Journal
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 3
SP - 677
EP - 686
AB - 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.
LA - eng
KW - strict Mittag-Leffler condition; locally split morphism; Gorenstein projective module; Ding projective module
UR - http://eudml.org/doc/294739
ER -

References

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  1. Hügel, L. Angeleri, Bazzoni, S., Herbera, D., 10.1090/S0002-9947-07-04255-9, Trans. Am. Math. Soc. 360 (2008), 2409-2421. (2008) Zbl1136.13005MR2373319DOI10.1090/S0002-9947-07-04255-9
  2. Hügel, L. Angeleri, Herbera, D., 10.1512/iumj.2008.57.3325, Indiana Univ. Math. J. 57 (2008), 2459-2517. (2008) Zbl1206.16002MR2463975DOI10.1512/iumj.2008.57.3325
  3. Azumaya, G., 10.1090/conm/124, Azumaya Algebras, Actions, and Modules Proc. Conf., Bloomington 1990, Contemp. Math. 124, Am. Math. Soc., Providence (1992), 17-22. (1992) Zbl0743.16003MR1144024DOI10.1090/conm/124
  4. Bazzoni, S., Herbera, D., 10.1007/s10468-007-9064-3, Algebr. Represent. Theory 11 (2008), 43-61. (2008) Zbl1187.16008MR2369100DOI10.1007/s10468-007-9064-3
  5. Bazzoni, S., Šťovíček, J., 10.1090/S0002-9939-07-08911-3, Proc. Am. Math. Soc. 135 (2007), 3771-3781. (2007) Zbl1132.16008MR2341926DOI10.1090/S0002-9939-07-08911-3
  6. Bennis, D., Mahdou, N., 10.1016/j.jpaa.2006.10.010, J. Pure Appl. Algebra 210 (2007), 437-445. (2007) Zbl1118.13014MR2320007DOI10.1016/j.jpaa.2006.10.010
  7. Chase, S. U., 10.2307/1993382, Trans. Am. Math. Soc. 97 (1960), 457-473. (1960) Zbl0100.26602MR0120260DOI10.2307/1993382
  8. Ding, N., Li, Y., Mao, L., 10.1017/S1446788708000761, J. Aust. Math. Soc. 86 (2009), 323-338. (2009) Zbl1200.16010MR2529328DOI10.1017/S1446788708000761
  9. Emmanouil, I., 10.1016/j.aim.2010.06.007, Adv. Math. 225 (2010), 3446-3462. (2010) Zbl1214.20050MR2729012DOI10.1016/j.aim.2010.06.007
  10. Emmanouil, I., Talelli, O., 10.1112/jlms/jdr014, J. Lond. Math. Soc., II. Ser. 84 (2011), 408-432. (2011) Zbl1237.16004MR2835337DOI10.1112/jlms/jdr014
  11. Enochs, E. E., Jenda, O. M. G., 10.1515/9783110803662, De Gruyter Expositions in Mathematics 30, Walter de Gruyter, Berlin (2000). (2000) Zbl0952.13001MR1753146DOI10.1515/9783110803662
  12. Gillespie, J., 10.4310/HHA.2010.v12.n1.a6, Homology Homotopy Appl. 12 (2010), 61-73. (2010) Zbl1231.16005MR2607410DOI10.4310/HHA.2010.v12.n1.a6
  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. (1995) Zbl0235.14007MR1611786
  14. Herbera, D., Trlifaj, J., 10.1016/j.aim.2012.02.013, Adv. Math. 229 (2012), 3436-3467. (2012) Zbl1279.16001MR2900444DOI10.1016/j.aim.2012.02.013
  15. Raynaud, M., Gruson, L., 10.1007/BF01390094, Invent. Math. 13 (1971), 1-89 French. (1971) Zbl0227.14010MR0308104DOI10.1007/BF01390094
  16. Zimmermann, W., 10.1016/S0022-4049(01)00011-1, J. Pure Appl. Algebra 166 (2002), 337-357. (2002) Zbl0993.16002MR1870625DOI10.1016/S0022-4049(01)00011-1

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