Radically Principal Ideal Rings

한국수학교육학회지시리즈B:순수및응용수학 / 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

장규환 (인천대학교)
천상민 (중앙대학교)

장규환, & 천상민. (2023). . 한국수학교육학회지시리즈B:순수및응용수학, 30(4), 397-406, https://doi.org/10.7468/jksmeb.2023.30.4.397

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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.

keywords: radically principal ideal ring, polynomial ring, PvMD

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논문 상세

Vol.30 No.4

Radically Principal Ideal Rings

Abstract

한국수학교육학회지시리즈B:순수및응용수학