报告地点:腾讯会议:69744317
报告人:Xavier Mary 教授
工作单位:Université Paris-Ouest Nanterre – La Défense
举办单位:スポーツ オンラインカジノ
报告人简介:Xavier Mary, 2006年博士毕业于巴黎大学。目前为法国巴黎第十大学教授,主要研究领域包括:半群理论、环论、代数等。X. Mary教授在国际代数领域享有很高的知名度,于2011年引入了“The inverse along an element”,现称之为Mary逆,被广泛的研究。目前国际上以Mary逆命名此逆。目前,X. Mary教授已在Linear Algebra Appl., Linear Multilinear Algebra, Appl. Math. Comput., Comm. Algebra J. Algebra Appl.等杂志上发表了30篇学术论文。并且,X. Mary教授主持过欧洲地平线2020项目。
报告1:On an equivalence between semigroups and certain categories with thin strict factorization systems-1
报告时间:2024年4月24日(星期三)15:30-16:30
报告简介:Since the seminal work of Nambooripad, there has been a growing interest in representations of semigroups by certain small categories. This led to the well-known equivalence between inverse semigroups and inductive groupoids (the Ehresmann-Schein-Nambooripad theorem), or the less-known equivalences between the category of regular semigroups, the category of regular inductive groupoids, and the category of cross-connections. In the talk, we will show how the Schützenberger category of a semigroup allows the construction of an equivalence between the category of semigroups and the category of small categories with a strict factorization system and a bimodule map. Taking natural transformations into account, this extends to an equivalence for a 2-category of unital semigroups. As an application, we will show that in this 2-categorical setting, 2-equivalence happens to be exactly Morita equivalence (of monoids).
报告2:On an equivalence between semigroups and certain categories with thin strict factorization systems-2
报告时间:2024年4月26日(星期五)15:30-16:30
报告简介:Since the seminal work of Nambooripad, there has been a growing interest in representations of semigroups by certain small categories. This led to the well-known equivalence between inverse semigroups and inductive groupoids (the Ehresmann-Schein-Nambooripad theorem), or the less-known equivalences between the category of regular semigroups, the category of regular inductive groupoids, and the category of cross-connections. In the talk, we will show how the Schützenberger category of a semigroup allows the construction of an equivalence between the category of semigroups and the category of small categories with a strict factorization system and a bimodule map. Taking natural transformations into account, this extends to an equivalence for a 2-category of unital semigroups. As an application, we will show that in this 2-categorical setting, 2-equivalence happens to be exactly Morita equivalence (of monoids).
报告3:Characterizations of clean elements-1
报告时间:2024年4月28日(星期日)15:30-16:30
报告简介:We characterize clean elements in unital and general rings by means of outer inverses. Some special cases, such as both clean and unit-regular elements, or strongly clean elements, are discussed. As an application, we also derive new characterizations of strongly regular elements.
报告4:Characterizations of clean elements-2
报告时间:2024年4月29日(星期一)15:30-16:30
报告简介:We characterize clean elements in unital and general rings by means of outer inverses. Some special cases, such as both clean and unit-regular elements, or strongly clean elements, are discussed. As an application, we also derive new characterizations of strongly regular elements.