Geodesic
Eine Charakterisierung der Menge Ass(u) in Kommutativen Noetherschen Ringen
Publications de l'Institut Mathématique, _N_S_33 (1983) no. 47, p. 179 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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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.
Classification : 13A17 13E05
Keywords: Noetherian commutative rings, primary decomposition of ideals, associated prime ideals 
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     author = {Veselin Peri\'c},
     title = {Eine {Charakterisierung} der {Menge} {Ass(u)} in {Kommutativen} {Noetherschen} {Ringen}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {179 },
     year = {1983},
     volume = {_N_S_33},
     number = {47},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1983_N_S_33_47_a25/}
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Veselin Perić. Eine Charakterisierung der Menge Ass(u) in Kommutativen Noetherschen Ringen. Publications de l'Institut Mathématique, _N_S_33 (1983) no. 47, p. 179 . http://geodesic.mathdoc.fr/item/PIM_1983_N_S_33_47_a25/