Resumen de A note on semistar Noetherian domains

Giampaolo Picozza

• We study semistar Noetherian domains, that is, domains having the ascending chain condition on "quasi semistar ideals''.We generalize several of the classical results that hold in Noetherian domains to the case of semistar operations stable and of finite type, for instance, Cohen Theorem, primary decomposition, principal ideal Theorem, Krull intersection Theorem, etc. We do this mainly by using a method that allows one to transfer properties already proved for star operations to the context of semistar operations. Furthermore, an analogue of the Hilbert basis Theorem for semistar Noetherian domain (with respect to stable semistar operations) is proved.