When the poset of normalized ideals of a numerical semigroup is a lattice
主 讲 人 ：Stefano BONZIO 副教授
活动时间：06月18日19时00分
地 点 ：伟德bv1946D311室 Zoon link: https://us06web.zoom.us/j/86763384947?pwd=qXhOzOcHvaaiw2jqADI8iqNavdgm14.1
讲座内容：
Given a numerical semigroup $S$, the set of its normalized ideals $\mathcal{I}_0(S)$ can be turned into a poset by the relation $\preceq$ defined as $I \preceq J$ if there exists a normalized ideal $K$ such that $I + K = J$.
In this talk, we characterize when the (finite) poset $(\mathcal{I}_0(S), \preceq)$ is a lattice, proving that this holds if and only if the multiplicity $m(S)$ of $S$ does not exceed four. Moreover, we will focus on the significance of the lattice $(\mathcal{I}_0(S), \preceq)$ for numerical semigroups of multiplicity three.
主讲人介绍：
Stefano Bonzio has been an Associate Professor at the Department of Mathematics of the University of Cagliari (Italy) since 2021. Before joining UniCA, he held research positions at the Spanish Research Council (as a Marie Curie fellow), the University of Turin, the Polytechnic University of the Marche, and the Czech Academy of Sciences.
He is a logician mainly working in non-classical logics and the interplay between logic and algebra, including the study of algebras of logic, algebraic logic, and universal algebra (in particular, the theory of Płonka sums). He has also conducted research in semigroup theory, specifically on numerical and Clifford semigroups.