代数表示论学术报告

报告题目：Coherency for monoids and purity for their acts

报告人：杨丹丹 教授（西安电子科技大学）

摘要：In this talk, we study the relationship between coherency of a monoid and purity properties of its acts. An underlying motivation comes from the following question for an algebra: when does the guaranteed solution of a finite consistent set of equations in one variable lift to the guarantee of solutions of finite consistent sets equations in any (finite) number of variables? This is a long-standing and intriguing problem, with a positive answer for some algebraic structures (e.g. groups and semigroups) but not fully understood for modules over rings or acts over monoids.

         Our first main result shows that for a right coherent monoid S the classes of almost pure and absolutely pure S-acts coincide. Our second main result is that a monoid S is right coherent if and only if the classes of mfp-pure and absolutely pure S-acts coincide. We give specific examples of monoids S that are not right coherent yet are such that the classes of almost pure and absolutely pure S-acts coincide. Finally we give a condition on a monoid S for all almost pure S-acts to be absolutely pure in terms of finitely presented S-acts, their finitely generated subacts, and certain canonical extensions.

报告时间：2023年3月14日（周二）下午2:00-3:00

线上报告地点：腾讯会议 ID：145 880 450

联系人： 惠昌常 陈红星