Abstract
Let D be an integral domain with quotient field K, X be an indeterminate over D, be the polynomial ring over K,
be an integer,
, where
, and
, i.e,
. Then Rn is a subring of
with total quotient ring
. In this paper, we study several ring-theoretic properties of Rn, with a focus on Prüfer rings and Prüfer v-multiplication rings (PvMRs). For example, we show when Rn is a Prüfer ring, a Bézout ring, a PvMR, or a GCD ring.
Acknowledgment
This work was supported by the Incheon National University Research Grant in 2022. The authors would like to thank the reviewer for his/her constructive feedback, which significantly improved the manuscript.