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The $u$-$S$-weak global dimensions of commutative rings

Xiaolei Zhang
대한수학회 (The Korean Mathematical Society)|2023.01|대한수학회논문집 (Communications of the KMS)|제38권 제1호|pp. 97-112|DOI 10.4134/CKMS.c220016

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키워드

polynomial ring$u$-$S$-flat module$u$-$S$-flat dimension$u$-$S$-weak global dimension
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초록

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.

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.

참고문헌 (7)

  1. D. D. Anderson, "S-Noetherian rings", Comm. Algebra, 30(9), pp.4407~4416 (2002)[DOI]
  2. L. Fuchs, "Modules over non-Noetherian domains, Mathematical Surveys and Monographs, 84" (2001), American Mathematical Society
  3. S. Glaz, "Commutative coherent rings", Lecture Notes in Mathematics, 1371 (1989), Springer-Verlag
  4. I. Kaplansky, "Commutative Rings" (1970), Allyn and Bacon, Inc
  5. F. Wang, "Foundations of commutative rings and their modules, Algebra and Applications, 22" (2016), Springer
  6. S. H. Zhang, "T-projective modules and G-semisimple rings", Acta Math. Sinica, 35(3), pp.378~386 (1992)
  7. X. L. Zhang, "Characterizing S-at modules and S-von Neumann regular rings by unifor-mity", Bull. Korean Math. Soc[DOI]

관련 논문AI추천

THE u-S-GLOBAL DIMENSIONS OF COMMUTATIVE RINGSWei Qi, Xiaolei Zhang대한수학회 · 대한수학회보2023 · 제60권 제6호Weak u-S-flat Modules and DimensionsRefat Abdelmawla Khaled Assaad, Xiaolei Zhang경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2023 · 제63권 제3호$\mathcal{F_{S}}$-Mittag-Leffler modules and global dimension relative to $\mathcal{F_{S}}$-Mittag-Leffler modulesFanggui Wang, Mingzhao Chen대한수학회 · 대한수학회보2019 · 제56권 제4호On uniformly $S$-absolutely pure modulesXiaolei Zhang대한수학회 · 대한수학회지2023 · 제60권 제3호ON 𝜙-w-FLAT MODULES AND THEIR HOMOLOGICAL DIMENSIONSWei Zhao, Xiaolei Zhang대한수학회 · 대한수학회보2021 · 제58권 제4호THE ω-WEAK GLOBAL DIMENSION OF COMMUTATIVE RINGSFanggui Wang, Lei Qiao대한수학회 · 대한수학회보2015 · 제52권 제4호

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