报告名称：Semigroups with finitely generated universal left congruence

报告专家：杨丹丹

专家所在单位：西安电子科技大学

报告时间：2021年9月10日 上午10：00-12：00

报告地点：数统学院 203

专家简介：杨丹丹，2014年获得英国约克大学的数学博士学位。现为西安电子科技大学教授，博导，华山学者。主要从事代数学方向的研究，解决了半群代数、组合群论中关于字问题的可解性、极大子群的分类等公开问题和猜想，相关成果发表于Adv.Math.、Quart. J. Math. (Oxford)、J. Algebra等期刊。曾获陕西青年科技奖、陕西省高校青年杰出人才称号。

报告摘要：We consider semigroups such that the universal left congruence ω^l is finitely

generated. Certainly a left noetherian semigroup, that is, one in which all left congruences are finitely generated, satisfies our condition. In the case of a monoid the condition that ω^l is finitely generated is equivalent to a number of pre-existing notions. In particular, a monoid satisfies the homological finiteness condition of being of type left-FP_1 exactly when ω^l is finitely generated.

Our investigations enable us to classify those semigroups such that ω^l is finitely generated that lie in certain important classes, such as strong semilattices of semigroups, inverse semigroups, Rees matrix semigroups (over semigroups) and completely regular semigroups. We consider closure properties for the class of semigroups such that ω^l is finitely generated, including under morphic image, direct product, semi-direct product, free product and o-direct union. Our work was inspired by the stronger condition, stated for monoids in the work of White, of being pseudo-finite. Where appropriate, we specialise our investigations to pseudo-finite semigroups and monoids. In particular, we answer a question of Dales and White concerning the nature of pseudo-finite monoids.

邀请人：刘合国

(审核：郑大彬）