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PULLBACKS OF 𝓒-HEREDITARY DOMAINS

  • Pu, Yongyan (College of Mathematics and Software Science Sichuan Normal University) ;
  • Tang, Gaohua (College of Mathematics and Statistics Guangxi Teacher's Education University) ;
  • Wang, Fanggui (College of Mathematics and Software Science Sichuan Normal University)
  • Received : 2017.07.10
  • Accepted : 2017.11.22
  • Published : 2018.07.31

Abstract

Let (RDTF, M) be a Milnor square. In this paper, it is proved that R is a ${\mathcal{C}}$-hereditary domain if and only if both D and T are ${\mathcal{C}}$-hereditary domains; R is an almost perfect domain if and only if D is a field and T is an almost perfect domain; R is a Matlis domain if and only if T is a Matlis domain. Furthermore, to give a negative answer to Lee, s question, we construct a counter example which is a C-hereditary domain R with $w.gl.dim(R)={\infty}$.

Keywords

References

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