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Special properties of Hurwitz series rings
Authors:Lunqun Ouyang  Kexin Zheng  Qiong Zhou  Yueming Xiang
Institution:1.Department of Mathematics,Hunan University of Science and Technology,Xiangtan,People’s Republic of China;2.Department of Mathematics and Applied Mathematics,Huaihua University,Huaihua,People’s Republic of China
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:
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