Special properties of Hurwitz series rings
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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.
KeywordsHurwitz series strongly Hopfian ring radical property
2000 Mathemetics Subject Classification13F25
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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