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THE w-WEAK GLOBAL DIMENSION OF COMMUTATIVE RINGS

  • WANG, FANGGUI ;
  • QIAO, LEI
  • Received : 2014.09.08
  • Published : 2015.07.31

Abstract

In this paper, we introduce and study the w-weak global dimension w-w.gl.dim(R) of a commutative ring R. As an application, it is shown that an integral domain R is a $Pr\ddot{u}fer$ v-multiplication domain if and only if w-w.gl.dim(R) ${\leq}1$. We also show that there is a large class of domains in which Hilbert's syzygy Theorem for the w-weak global dimension does not hold. Namely, we prove that if R is an integral domain (but not a field) for which the polynomial ring R[x] is w-coherent, then w-w.gl.dim(R[x]) = w-w.gl.dim(R).

Keywords

GV-torsionfree module;w-module;w-flat module;w-flat dimension;w-weak global dimension

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  3. A new application of boundary integral behaviors of harmonic functions to the least harmonic majorant vol.2017, pp.1, 2017, https://doi.org/10.1186/s13661-017-0798-5
  4. Purity over Prüfer v-multiplication domains, II pp.1793-6829, 2018, https://doi.org/10.1142/S0219498818502237
  5. -Flat Modules and Dimensions vol.25, pp.02, 2018, https://doi.org/10.1142/S1005386718000147
  6. A homological characterization of Krull domains II pp.1532-4125, 2019, https://doi.org/10.1080/00927872.2018.1524007

Acknowledgement

Supported by : NSFC