Abstract
Let D be an integral domain with quotient field K, \(\Gamma \) a nonzero torsion-free grading monoid and \(\Gamma ^*=\Gamma {\setminus } \{0\}\). In this paper, we characterize when the semigroup ring \(D[\Gamma ]\) is an almost Prüfer v-multiplication domain or an almost Prüfer domain. We also give an equivalent condition for the composite semigroup ring \(D+K[\Gamma ^*]\) to be an almost Prüfer v-multiplication domain or an almost Prüfer domain when \(\Gamma \cap -\Gamma =\{0\}\).
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Acknowledgements
We would like to thank the referee for his/her several valuable suggestions. The first author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2014R1A1A1002478). The second author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2014R1A1A2054132).
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Communicated by László Márki.
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Lim, J.W., Oh, D.Y. Semigroup rings as almost Prüfer v-multiplication domains. Semigroup Forum 97, 53–63 (2018). https://doi.org/10.1007/s00233-017-9898-x
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DOI: https://doi.org/10.1007/s00233-017-9898-x