Special properties of Hurwitz series rings |
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Authors: | Lunqun Ouyang Kexin Zheng Qiong Zhou Yueming Xiang |
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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 |
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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. |
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