主 讲 人 ：Laura Cossu    助理教授

活动时间：2025-09-21 15:20:00

地      点 ：数学科学学院D203报告厅(Zoom: https://us06web.zoom.us/j/86763384947?pwd=qXhOzOcHvaaiw2jqADI8iqNavdgm14.1, ID: 86763384947; passcode: 612593)

主办单位：数学科学学院

讲座内容：

Let $H$ be any multiplicative monoid, and consider the collection of all its finite subsets that contain the identity element. This collection forms a monoid under setwise multiplication, known as the reduced power monoid of $H$ and denoted by $\mathcal P_{{\rm fin},1}(H)$. Since $\mathcal P_{{\rm fin},1}(H)$ is non-cancellative whenever $H$ is nontrivial, it serves as a central example in the study of a newly developed general theory of factorization. This theory, recently introduced by Cossu and Tringali, investigates decompositions into (almost) arbitrary factors within monoids that may admit nontrivial idempotents. Within this framework, we focus on minimal factorizations into irreducible elements in reduced power monoids. Among other results, we will discuss necessary and sufficient conditions on $H$ under which $\mathcal P_{{\rm fin},1}(H)$ admits 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 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. She has also been a visiting researcher at New Mexico State University (NM, USA), University of California, Irvine (CA, 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. She has published in various international journals, including J. London Math. Soc., Israel J. Math., and J. Algebra.