Nakayama's lemma and applications

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

We give two versions of Nakayama's lemma in the context of commutative rings and some applications, in particular, we prove two versions of Krull's intersection theorem. To do so, we will use the Artin-Rees lemma, for which we will give a detailed proof. We will suppose that all rings are commutative with identity.

Domaines: Anneaux et algèbres [math.RA]

Rodney Coleman, Laurent Zwald. Nakayama's lemma and applications. 2020. ⟨hal-03040587⟩