Articles written in Proceedings – Mathematical Sciences
Volume 128 Issue 4 September 2018 Article ID 0045 Research Article
In this paper, we study some properties of the Hurwitz series ring $H R$ (resp. Hurwitz polynomial ring $h R$), such as the flatness or the faithful flatness of $H R/(f)$ (resp. $h R/(f)$), the strongly Hopfian property and the radical property of $H R$ (resp. $h R$). We give some sufficient and necessary conditions for $H R/(f)$ (resp. $h R/(f)$) to be flat or faithful flat. We also prove that the strongly Hopfian property transfer between$R$ and $H R$ (resp. $h R$), and some radicals of $H R$ can be determined in terms of those of $R$, in case $R$ satisfies some additional conditions.
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