Dario Spirito

Some topological considerations on semistar operations

Abstract We consider properties and applications of a new topology, called the Zariski topology, on the space SStar ( A ) of all the semistar operations on an integral domain A. We prove that the set of all overrings of A, endowed with the classical Zariski topology, is homeomorphic to a subspace of SStar ( A ) . The topology on SStar ( A ) provides a general theory, through which we see several algebraic properties of semistar operation as very particular cases of our construction. Moreover, we show that the subspace SStar f ( A ) of all the semistar operations of finite type on A is a spectral space.

Star Operations on Numerical Semigroups

It is proved that the number of numerical semigroups with a fixed number n of star operations is finite if n > 1. The result is then extended to the class of analytically irreducible residually rational one-dimensional Noetherian rings with finite residue field and integral closure equal to a fixed discrete valuation domain.

Towards a classification of stable semistar operations on a Prüfer domain

ABSTRACT We study stable semistar operations defined over a Prüfer domain, showing that, if every ideal of a Prüfer domain R has only finitely many minimal primes, every such closure can be described through semistar operations defined on valuation overrings of R.

EMBEDDING THE SET OF NON-DIVISORIAL IDEALS OF A NUMERICAL SEMIGROUP INTO ℕn

The set 𝒢0(S) of the classes of nondivisorial ideals of a numerical semigroup S can be endowed with a natural partial order induced by the set of star operations on S. We study embeddings of 𝒢0(S) ...