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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.30 No.4

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Radically Principal Ideal Rings

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2023, v.30 no.4, pp.397-406
https://doi.org/10.7468/jksmeb.2023.30.4.397


& (2023). Radically Principal Ideal Rings. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 30(4), 397-406, https://doi.org/10.7468/jksmeb.2023.30.4.397

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.

keywords
radically principal ideal ring, polynomial ring, PvMD

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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