Prof. Giuseppina Terzo, from Università degli Studi di Napoli “Federico II”., will give a seminar on Wednesday 3 May 2023 at 14:30 in Sala Riunioni, DipMat.
Title: Exponential ideals in an exponential polynomial ring.
When we work with exponential polynomial rings over an exponential field some classical results fail, as Hilbert’s Basis Theorem and Nullstellensatz. We will present some results on exponential ideals in exponential rings, in order to see if some weak version of Nullstellensatz holds. Among E-ideals three categories stand out: E-prime ideals; E-ideals which are maximal as ideals, which we will call “strongly maximal”; E-ideals which are maximals among E-ideals, which we will call “E-maximal”. We want to study these three categories of E-ideals in an exponential polynomial ring over an exponential domain. We show that, except for the obvious implications, i.e. strongly maximal implies E-prime and E-maximal, the three notions are independent. We introduce also the notion of radical E-ideal and we give a characterization of it.