대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제60권2호
  • /
  • Pages.405-423
  • /
  • 2023
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

MODEL STRUCTURES AND RECOLLEMENTS INDUCED BY DUALITY PAIRS

  • Wenjing Chen (Department of Mathematics Northwest Normal University) ;
  • Ling Li (Department of Mathematics Northwest Normal University) ;
  • Yanping Rao (Department of Mathematics Northwest Normal University)
  • 투고 : 2022.03.02
  • 심사 : 2022.09.22
  • 발행 : 2023.03.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

Let (𝓛, 𝒜) be a complete duality pair. We give some equivalent characterizations of Gorenstein (𝓛, 𝒜)-projective modules and construct some model structures associated to duality pairs and Frobenius pairs. Some rings are described by Frobenius pairs. In addition, we investigate special Gorenstein (𝓛, 𝒜)-projective modules and construct some model structures and recollements associated to them.

키워드

과제정보

The authors sincerely thank the referee for the helpful suggestions and valuable comments. This work was supported by National Natural Science Foundation of China (Nos. 11761060, 11901463), Science and Technology Project of Gansu Province (20JR5RA517), Innovation Ability Enhancement Project of Gansu Higher Education Institutions (2019A-002) and Improvement of Young Teachers' Scientific Research Ability (NWNU-LKQN-18-30).

참고문헌

  1. V. Becerril, O. Mendoza, M. A. Perez, and V. Santiago, Frobenius pairs in abelian categories. Correspondences with cotorsion pairs, exact model categories, and Auslander-Buchweitz contexts, J. Homotopy Relat. Struct. 14 (2019), no. 1, 1-50. https://doi.org/10.1007/s40062-018-0208-4 
  2. A. A. Beilinson, J. Bernstein, and P. Deligne, Faisceaux pervers, in Analysis and topology on singular spaces, I (Luminy, 1981), 5-171, Asterisque, 100, Soc. Math. France, Paris, 1982. 
  3. D. Bravo, J. Gillespie, and M. Hovey, The stable module category of a general ring, arXiv:1405.5768, 2014. 
  4. T. Buhler, Exact categories, Expo. Math. 28 (2010), no. 1, 1-69. https://doi.org/10.1016/j.exmath.2009.04.004 
  5. W. Chen, Z. Liu, and X. Yang, A new method to construct model structures from a cotorsion pair, Comm. Algebra 47 (2019), no. 11, 4420-4431. https://doi.org/10.1080/00927872.2018.1527922 
  6. N. Ding, Y. Li, and L. Mao, Strongly Gorenstein flat modules, J. Aust. Math. Soc. 86 (2009), no. 3, 323-338. https://doi.org/10.1017/S1446788708000761 
  7. E. E. Enochs and O. M. G. Jenda, Gorenstein injective and projective modules, Math. Z. 220 (1995), no. 4, 611-633. https://doi.org/10.1007/BF02572634 
  8. E. E. Enochs and O. M. G. Jenda, Relative Homological Algebra, De Gruyter Expositions in Mathematics, 30, Walter de Gruyter & Co., Berlin, 2000. https://doi.org/10.1515/9783110803662 
  9. E. E. Enochs and O. M. G. Jenda, Relative Homological Algebra. Volume 2, De Gruyter Expositions in Mathematics, 54, Walter de Gruyter GmbH & Co. KG, Berlin, 2011. 
  10. J. Gillespie, Model structures on exact categories, J. Pure Appl. Algebra 215 (2011), no. 12, 2892-2902. https://doi.org/10.1016/j.jpaa.2011.04.010 
  11. J. Gillespie, How to construct a Hovey triple from two cotorsion pairs, Fund. Math. 230 (2015), no. 3, 281-289. https://doi.org/10.4064/fm230-3-4 
  12. J. Gillespie, Gorenstein complexes and recollements from cotorsion pairs, Adv. Math. 291 (2016), 859-911. https://doi.org/10.1016/j.aim.2016.01.004 
  13. J. Gillespie, Duality pairs and stable module categories, J. Pure Appl. Algebra 223 (2019), no. 8, 3425-3435. https://doi.org/10.1016/j.jpaa.2018.11.010 
  14. J. Gillespie and A. Iacob, Duality pairs, generalized Gorenstein modules, and Ding injective envelopes, C. R. Math. Acad. Sci. Paris 360 (2022), 381-398. https://doi.org/10.5802/crmath.306 
  15. R. Gobel and J. Trlifaj, Approximations and Endomorphism Algebras of Modules. Volume 2, second revised and extended edition, De Gruyter Expositions in Mathematics, 41, Walter de Gruyter GmbH & Co. KG, Berlin, 2012. https://doi.org/10.1515/9783110218114 
  16. H. Holm and P. Jorgensen, Cotorsion pairs induced by duality pairs, J. Commut. Algebra 1 (2009), no. 4, 621-633. https://doi.org/10.1216/JCA-2009-1-4-621 
  17. M. Hovey, Cotorsion pairs, model category structures, and representation theory, Math. Z. 241 (2002), no. 3, 553-592. https://doi.org/10.1007/s00209-002-0431-9 
  18. B. Keller, Derived categories and their uses, in Handbook of algebra, Vol. 1, 671-701, Handb. Algebr., 1, Elsevier/North-Holland, Amsterdam, 1996. https://doi.org/10.1016/S1570-7954(96)80023-4 
  19. Z. Wang, G. Yang, and R. Zhu, Gorenstein flat modules with respect to duality pairs, Comm. Algebra 47 (2019), no. 12, 4989-5006. https://doi.org/10.1080/00927872.2019.1609011 
  20. X. Yang and W. Chen, Relative homological dimensions and Tate cohomology of complexes with respect to cotorsion pairs, Comm. Algebra 45 (2017), no. 7, 2875-2888. https://doi.org/10.1080/00927872.2016.1233226