Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON 𝜙-w-FLAT MODULES AND THEIR HOMOLOGICAL DIMENSIONS

  • Zhang, Xiaolei (Department of Basic Courses Chengdu Aeronautic Polytechnic) ;
  • Zhao, Wei (School of Mathematics ABa Teachers University)
  • Received : 2020.09.23
  • Accepted : 2021.01.29
  • Published : 2021.07.31
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Abstract

In this paper, we introduce and study the class of 𝜙-w-flat modules which are generalizations of both 𝜙-flat modules and w-flat modules. The 𝜙-w-weak global dimension 𝜙-w-w.gl.dim(R) of a commutative ring R is also introduced and studied. We show that, for a 𝜙-ring R, 𝜙-w-w.gl.dim(R) = 0 if and only if w-dim(R) = 0 if and only if R is a 𝜙-von Neumann ring. It is also proved that, for a strongly 𝜙-ring R, 𝜙-w-w.gl.dim(R) ≤ 1 if and only if each nonnil ideal of R is 𝜙-w-flat, if and only if R is a 𝜙-PvMR, if and only if R is a PvMR.

Keywords

Acknowledgement

The first author was supported by the Natural Science Foundation of Chengdu Aeronautic Polytechnic (No. 062026). The second author was supported by the National Natural Science Foundation of China (No. 12061001).

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