Geodesic
The Ordering of Spec R
Canadian journal of mathematics, Tome 28 (1976) no. 4, pp. 820-835

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

Let Specie denote the set of prime ideals of a commutative ring with identity R, ordered by inclusion; and call a partially ordered set spectral if it is order isomorphic to Spec R for some R. What are some conditions, necessary or sufficient, for a partially ordered set X to be spectral? The most desirable answer would be the type of result that would allow one to stare at the diagram of a given X and then be able to say whether or not X is spectral. For example, it is known that finite partially ordered sets are spectral (see [2] or [5]). 
Lewis, William J.; Ohm, Jack. The Ordering of Spec R. Canadian journal of mathematics, Tome 28 (1976) no. 4, pp. 820-835. doi: 10.4153/CJM-1976-079-2
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[1] 1. Cox, S. H. and Pendleton, R. L., Rings for which certain flat modules are projective, Trans. Amer. Math. Soc. 150 (1970), 139–156. Google Scholar

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