Miscellaneous results on prime ideals

Rodney Coleman (1) , Laurent Zwald (2)

1 CASC - Calcul Algébrique et Symbolique, Sécurité, Systèmes Complexes, Codes et Cryptologie
2 SVH - Statistique pour le Vivant et l’Homme

In these notes, we present various useful results concerning prime ideals. We characterize prime and maximal ideals in Z[X] and introduce the height of an ideal and the dimension of a ring. In particular, we provide bounds for the dimension of a polynomial ring. We also study in detail radicals and certain proprieties of artinian and noetherian rings. We give a proof of the prime avoidance lemma.

Domaines: Anneaux et algèbres [math.RA]

Rodney Coleman, Laurent Zwald. Miscellaneous results on prime ideals. 2020. ⟨hal-03040598⟩