Primary 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

We introduce primary ideals and prove the Lasker-Noether theorem, namely that in a noetherian ring any ideal can be written as a minimal finite intersection of primary ideals. We also introduce minimal prime ideals and symbolic powers of prime ideals, which are closely related to primary ideals.

Domaines: Anneaux et algèbres [math.RA]

Rodney Coleman, Laurent Zwald. Primary ideals. 2020. ⟨hal-03040606⟩