PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 33(47), pp. 179185 (1983) 

EINE CHARAKTERISIERUNG DER MENGE Ass$(\frak U)$ IN KOMMUTATIVEN NOETHERSCHEN RINGENVeselin Peri\'cPrirodnomatematicki fakultet, 71000 Sarajevo, JugoslavijaAbstract: Let $R$ be a commutative noetherian ring. For any ideal $\frak U$ of $R$ the set Ass$(\frak U)$ of all associated prime ideals of $\frak U$ is a finite set $P$ of prime ideals of $R$. If a finite set $P$ of prime ideals of $R$ contains no prime ideal of the height 0, i.e., no minimal prime ideal of $(0)$, then it is well known that there exists an ideal $\frak U$ of $R$ such that $P= \text{Ass}(\frak U)$ [1, 9.1]. It seems to be unknown what the precise necessary and sufficient condition is, on a finite set $P$ of primes, for the existence of such an ideal $\frak U$ [1, p. 68]. We answer here this question. Keywords: Noetherian commutative rings, primary decomposition of ideals, associated prime ideals Classification (MSC2000): 13A17, 13E05 Full text of the article:
Electronic fulltext finalized on: 3 Nov 2001. This page was last modified: 16 Nov 2001.
© 2001 Mathematical Institute of the Serbian Academy of Science and Arts
