Arithmetic of reduced power monoids
主 讲 人 ：Laura Cossu 助理教授
活动时间：12月19日19时00分
地 点 ：数学科学学院D203报告厅（Zoom 会议： https://us06web.zoom.us/j/84475767730?pwd=nSJeFrqBeJzesc3EMCO6pbwhLBdMtD.1 （会议号: 844 7576 7730 ；密码: 090149）
讲座内容：
If we take any multiplicative monoid $H$ and consider all its finite subsets that include the identity, these subsets form a monoid under setwise multiplication, which we call the reduced power monoid $\mathcal P_{{\rm fin},1}(H)$. This talk explores key arithmetic properties of reduced power monoids, taking into account the possible presence of nontrivial idempotents. For this purpose, we consider minimal factorizations into irreducibles, a concept that has recently been introduced in the abstract context of a novel general theory of factorization. Among other things, we will provide necessary and sufficient conditions on $H$ for $\mathcal P_{{\rm fin},1}(H)$ to admit unique minimal factorizations.
主讲人介绍：
Laura Cossu is a tenure-track Assistant Professor in the Department of Mathematics and Computer Science at the University of Cagliari, Italy. She received her Ph.D. in Mathematics from the University of Padua (Italy) in October 2017. She worked as a postdoctoral researcher in Padua and then at the University of Graz (Austria), where she was supported by various grants, including a Marie Skłodowska-Curie Individual Fellowship from the European Commission and a Principal Investigator project from the Austrian Science Fund. Dr. Cossu has also been a visiting researcher at New Mexico State University (NM, USA), Montclair State University (NJ, USA), and the Université Catholique de Louvain (Belgium). Her research interests include commutative and non-commutative ring and semigroup theory, factorization theory, and commutative algebra.
发布时间：2024-12-19 15:03:23
