Gorenstein projective complexes with respect to cotorsion pairs

Renyu Zhao; Pengju Ma

Czechoslovak Mathematical Journal (2019)

  • Volume: 69, Issue: 1, page 117-129
  • ISSN: 0011-4642

Abstract

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Let ( 𝒜 , ℬ ) be a complete and hereditary cotorsion pair in the category of left R -modules. In this paper, the so-called Gorenstein projective complexes with respect to the cotorsion pair ( 𝒜 , ℬ ) are introduced. We show that these complexes are just the complexes of Gorenstein projective modules with respect to the cotorsion pair ( 𝒜 , ℬ ) . As an application, we prove that both the Gorenstein projective modules with respect to cotorsion pairs and the Gorenstein projective complexes with respect to cotorsion pairs possess stability.

How to cite

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Zhao, Renyu, and Ma, Pengju. "Gorenstein projective complexes with respect to cotorsion pairs." Czechoslovak Mathematical Journal 69.1 (2019): 117-129. <http://eudml.org/doc/294760>.

@article{Zhao2019,
abstract = {Let $(\mathcal \{A,B\})$ be a complete and hereditary cotorsion pair in the category of left $R$-modules. In this paper, the so-called Gorenstein projective complexes with respect to the cotorsion pair $(\mathcal \{A\}, \mathcal \{B\})$ are introduced. We show that these complexes are just the complexes of Gorenstein projective modules with respect to the cotorsion pair $(\mathcal \{A\}, \mathcal \{B\})$. As an application, we prove that both the Gorenstein projective modules with respect to cotorsion pairs and the Gorenstein projective complexes with respect to cotorsion pairs possess stability.},
author = {Zhao, Renyu, Ma, Pengju},
journal = {Czechoslovak Mathematical Journal},
keywords = {cotorsion pair; Gorenstein projective complex with respect to cotorsion pairs; stability of Gorenstein categories},
language = {eng},
number = {1},
pages = {117-129},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Gorenstein projective complexes with respect to cotorsion pairs},
url = {http://eudml.org/doc/294760},
volume = {69},
year = {2019},
}

TY - JOUR
AU - Zhao, Renyu
AU - Ma, Pengju
TI - Gorenstein projective complexes with respect to cotorsion pairs
JO - Czechoslovak Mathematical Journal
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 1
SP - 117
EP - 129
AB - Let $(\mathcal {A,B})$ be a complete and hereditary cotorsion pair in the category of left $R$-modules. In this paper, the so-called Gorenstein projective complexes with respect to the cotorsion pair $(\mathcal {A}, \mathcal {B})$ are introduced. We show that these complexes are just the complexes of Gorenstein projective modules with respect to the cotorsion pair $(\mathcal {A}, \mathcal {B})$. As an application, we prove that both the Gorenstein projective modules with respect to cotorsion pairs and the Gorenstein projective complexes with respect to cotorsion pairs possess stability.
LA - eng
KW - cotorsion pair; Gorenstein projective complex with respect to cotorsion pairs; stability of Gorenstein categories
UR - http://eudml.org/doc/294760
ER -

References

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  1. Bouchiba, S., 10.1142/S100538671300059X, Algebra Colloq. 20 (2013), 623-636. (2013) Zbl1281.16010MR3116791DOI10.1142/S100538671300059X
  2. Bouchiba, S., Khaloui, M., 10.1017/S0017089511000516, Glasg. Math. J. 54 (2012), 169-175. (2012) Zbl1235.16009MR2862395DOI10.1017/S0017089511000516
  3. Bravo, D., Gillespie, J., 10.1080/00927872.2015.1044100, Commun. Algebra 44 (2016), 2213-2233. (2016) Zbl1346.18021MR3490674DOI10.1080/00927872.2015.1044100
  4. Enochs, E. E., Rozas, J. R. García, 10.1080/00927879808826229, Commun. Algebra 26 (1998), 1657-1674. (1998) Zbl0908.18007MR1622438DOI10.1080/00927879808826229
  5. Enochs, E. E., Jenda, O. M. G., 10.1007/BF02572634, Math. Z. 220 (1995), 611-633. (1995) Zbl0845.16005MR1363858DOI10.1007/BF02572634
  6. 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
  7. Rozas, J. R. García, Covers and Envelopes in the Category of Complexes of Modules, Chapman & Hall/CRC Research Notes in Mathematics 407, Chapman & Hall/CRC, Boca Raton (1999). (1999) Zbl0922.16001MR1693036
  8. Gillespie, J., 10.1090/S0002-9947-04-03416-6, Trans. Am. Math. Soc. 356 (2004), 3369-3390. (2004) Zbl1056.55011MR2052954DOI10.1090/S0002-9947-04-03416-6
  9. Holm, H., 10.1016/j.jpaa.2003.11.007, J. Pure Appl. Algebra 189 (2004), 167-193. (2004) Zbl1050.16003MR2038564DOI10.1016/j.jpaa.2003.11.007
  10. Hu, J. S., Xu, A. M., 10.1142/S1005386716000286, Algebra Colloq. 23 (2016), 251-262. (2016) Zbl1346.16006MR3475049DOI10.1142/S1005386716000286
  11. Liang, L., Ding, N. Q., Yang, G., 10.1007/s10114-014-3227-z, Acta Math. Sin., Engl. Ser. 30 (2014), 2063-2078. (2014) Zbl1304.18032MR3285935DOI10.1007/s10114-014-3227-z
  12. Sather-Wagstaff, S., Sharif, T., White, D., 10.1112/jlms/jdm124, J. Lond. Math. Soc., II. Ser. 77 (2008), 481-502. (2008) Zbl1140.18010MR2400403DOI10.1112/jlms/jdm124
  13. Xu, A. M., Ding, N. Q., 10.1080/00927872.2012.677892, Commun. Algebra 42 (2013), 3793-3804. (2013) Zbl1284.16006MR3169490DOI10.1080/00927872.2012.677892
  14. Yang, G., Liu, Z. K., 10.1017/S0013091510000489, Proc. Edinb. Math. Soc., II. Ser. 54 (2011), 783-797. (2011) Zbl1238.13023MR2837480DOI10.1017/S0013091510000489
  15. Yang, G., K.Liu, Z., 10.1017/S0017089511000528, Glasg. Math. J. 54 (2012), 177-191. (2012) Zbl1248.16007MR2862396DOI10.1017/S0017089511000528
  16. Yang, X. Y., Chen, W. J., 10.1080/00927872.2016.1233226, Commun. Algebra 45 (2017), 2875-2888. (2017) Zbl1372.18015MR3594565DOI10.1080/00927872.2016.1233226
  17. Yang, X. Y., Ding, N. Q., 10.1515/forum-2013-6014, Forum Math. 27 (2015), 3205-3231. (2015) Zbl1347.18003MR3420339DOI10.1515/forum-2013-6014
  18. Yang, X. Y., Liu, Z. K., 10.1080/00927871003741497, Commun. Algebra 39 (2011), 1705-1721. (2011) Zbl1238.16002MR2821502DOI10.1080/00927871003741497

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