The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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RADICALLY PRINCIPAL IDEAL RINGS

  • Gyu Whan Chang (Department of Mathematics Education, Incheon National University) ;
  • Sangmin Chun (Da Vinci College of General Education, Chung-Ang University)
  • Received : 2023.04.15
  • Accepted : 2023.06.10
  • Published : 2023.11.30
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Abstract

Let R be a commutative ring with identity, X be an indeterminate over R, and R[X] be the polynomial ring over R. In this paper, we study when R[X] is a radically principal ideal ring. We also study the t-operation analog of a radically principal ideal domain, which is said to be t-compactly packed. Among them, we show that if R is an integrally closed domain, then R[X] is t-compactly packed if and only if R is t-compactly packed and every prime ideal Q of R[X] with Q ∩ R = (0) is radically principal.

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Acknowledgement

The authors would like to thank the anonymous referee for his/her helpful comments and useful suggestions which improved the original version of this paper greatly. Chang was supported by the Incheon National University research grant in 2021.

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