Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

THE u-S-WEAK GLOBAL DIMENSIONS OF COMMUTATIVE RINGS

  • Xiaolei Zhang (School of Mathematics and Statistics Shandong University of Technology)
  • Received : 2022.01.25
  • Accepted : 2022.05.25
  • Published : 2023.01.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we introduce and study the u-S-weak global dimension u-S-w.gl.dim(R) of a commutative ring R for some multiplicative subset S of R. Moreover, the u-S-weak global dimensions of factor rings and polynomial rings are investigated.

Keywords

References

  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. L. Fuchs and L. Salce, Modules over non-Noetherian domains, Mathematical Surveys and Monographs, 84, American Mathematical Society, Providence, RI, 2001. https://doi.org/10.1090/surv/084
  3. S. Glaz, Commutative coherent rings, Lecture Notes in Mathematics, 1371, SpringerVerlag, Berlin, 1989. https://doi.org/10.1007/BFb0084570
  4. I. Kaplansky, Commutative Rings, Allyn and Bacon, Inc., Boston, MA, 1970.
  5. 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
  6. S. H. Zhang, T-projective modules and G-semisimple rings, Acta Math. Sinica 35 (1992), no. 3, 378-386.
  7. X. L. Zhang, Characterizing S-flat modules and S-von Neumann regular rings by uniformity, to appear in Bull. Korean Math. Soc. https://arxiv.org/abs/2105.07941. 105.07941