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Special properties of Hurwitz series rings

  • Lunqun Ouyang
  • Kexin Zheng
  • Qiong Zhou
  • Yueming Xiang
Article
  • 51 Downloads

Abstract

In this paper, we study some properties of the Hurwitz series ring HR (resp. Hurwitz polynomial ring hR), such as the flatness or the faithful flatness of HR / (f) (resp. hR / (f)), the strongly Hopfian property and the radical property of HR (resp. hR). We give some sufficient and necessary conditions for HR / (f) (resp. hR / (f)) to be flat or faithful flat. We also prove that the strongly Hopfian property transfer between R and HR (resp. hR), and some radicals of HR can be determined in terms of those of R, in case R satisfies some additional conditions.

Keywords

Hurwitz series strongly Hopfian ring radical property 

2000 Mathemetics Subject Classification

13F25 

Notes

Acknowledgements

This research is supported by the National Natural Science Foundation of China (11471108), the Natural Science Foundation of Hunan Province (2016JJ2050), the Scientific Research Foundation of Hunan Provincial Education Department (12B101) and the Teaching Reform Foundation of Hunan Province (G21316).

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Copyright information

© Indian Academy of Sciences 2018

Authors and Affiliations

  • Lunqun Ouyang
    • 1
  • Kexin Zheng
    • 1
  • Qiong Zhou
    • 1
  • Yueming Xiang
    • 2
  1. 1.Department of MathematicsHunan University of Science and TechnologyXiangtanPeople’s Republic of China
  2. 2.Department of Mathematics and Applied MathematicsHuaihua UniversityHuaihuaPeople’s Republic of China

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