대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제60권6호
  • /
  • Pages.1523-1537
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  • 2023
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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THE u-S-GLOBAL DIMENSIONS OF COMMUTATIVE RINGS

  • Wei Qi (School of Mathematics and Statistics Shandong University of Technology) ;
  • Xiaolei Zhang (School of Mathematics and Statistics Shandong University of Technology)
  • 투고 : 2022.09.29
  • 심사 : 2023.08.14
  • 발행 : 2023.11.30
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초록

Let R be a commutative ring with identity and S a multiplicative subset of R. First, we introduce and study the u-S-projective dimension and u-S-injective dimension of an R-module, and then explore the u-S-global dimension u-S-gl.dim(R) of a commutative ring R, i.e., the supremum of u-S-projective dimensions of all R-modules. Finally, we investigate u-S-global dimensions of factor rings and polynomial rings.

키워드

과제정보

The first author was supported by National Natural Science Foundation of China (No. 12201361).

참고문헌

  1. D. D. Anderson and T. Dumitrescu, S-Noetherian rings, Comm. Algebra 30 (2002), no. 9, 4407-4416. https://doi.org/10.1081/AGB-120013328 
  2. W. Qi, H. Kim, F. G. Wang, M. Z. Chen, and W. Zhao. Uniformly S-Noetherian rings, submitted, https://arxiv.org/abs/2201.07913. 
  3. F. Wang and H. Kim, Foundations of commutative rings and their modules, Algebra and Applications, 22, Springer, Singapore, 2016. https://doi.org/10.1007/978-981-10-3337-7 
  4. X. Zhang, Characterizing S-flat modules and S-von Neumann regular rings by uniformity, Bull. Korean Math. Soc. 59 (2022), no. 3, 643-657. https://doi.org/10.4134/BKMS.b210291 
  5. X. Zhang, The u-S-weak global dimensions of commutative rings, Commun. Korean Math. Soc. 38 (2023), no. 1, 97-112. https://doi.org/10.4134/CKMS.c220016 
  6. X. Zhang, On uniformly S-coherent rings, submitted, https://arxiv.org/abs/2205.07137. 
  7. X. Zhang and W. Qi, Characterizing S-projective modules and S-semisimple rings by uniformity, J. Commut. Algebra 15 (2023), no. 1, 139-149. https://doi.org/10.1216/jca.2023.15.139