descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1966 English Publisher:Canadian Mathematical SocietyJournal:Canadian Journal of Mathematics, volume 18, pages 1,183-1,195 (issn: 0008-414X, eissn: 1496-4279,

Authors: Butts, H. S.; Gilmer, R. W. jun.;

doi: 10.4153/cjm-1966-117-9

Primary Ideals and Prime Power Ideals

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Abstract

This paper is concerned with the ideal theory of a commutative ringR.We sayRhas Property (α) if each primary ideal inRis a power of its (prime) radical;Ris said to have Property (δ) provided every ideal inRis an intersection of a finite number of prime power ideals. In (2, Theorem 8, p. 33) it is shown that ifDis a Noetherian integral domain with identity and if there are no ideals properly between any maximal ideal and its square, thenDis a Dedekind domain. It follows from this that ifDhas Property (α) and is Noetherian (in which caseDhas Property (δ)), thenDis Dedekind.

Keywords

commutative algebra

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