Geodesic
Primary Ideals and Prime Power Ideals
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 1183-1195

Voir la notice de l'article provenant de la source Cambridge University Press

This paper is concerned with the ideal theory of a commutative ring R. We say R has Property (α) if each primary ideal in R is a power of its (prime) radical; R is said to have Property (δ) provided every ideal in R is an intersection of a finite number of prime power ideals. In (2, Theorem 8, p. 33) it is shown that if D is a Noetherian integral domain with identity and if there are no ideals properly between any maximal ideal and its square, then D is a Dedekind domain. It follows from this that if D has Property (α) and is Noetherian (in which case D has Property (δ)), then D is Dedekind. 
Butts, H. S.; Jr., Robert W. Gilmer. Primary Ideals and Prime Power Ideals. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 1183-1195. doi: 10.4153/CJM-1966-117-9
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