Geodesic
Prime and maximal ideals in polynomial rings
Glasgow mathematical journal, Tome 37 (1995) no. 3, pp. 351-362

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

In this paper we study prime and maximal ideals in a polynomial ring R[X], where R is a ring with identity element. It is well-known that to study many questions we may assume Ris prime and consider just R-disjoint ideals. We give a characterizaton for an R-disjoint ideal to be prime. We study conditions under which there exists an R-disjoint ideal which is a maximal ideal and when this is the case how to determine all such maximal ideals. Finally, we prove a theorem giving several equivalent conditions for a maximal ideal to be generated by polynomials of minimal degree. 
Ferrero, Miguel. Prime and maximal ideals in polynomial rings. Glasgow mathematical journal, Tome 37 (1995) no. 3, pp. 351-362. doi: 10.1017/S0017089500031633
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