报告名称：Semiring varieties generated by finite fields and distributive lattices

主办单位：数学与统计学学院

报告专家：邵勇教授

专家所在单位：西北大学

报告时间：2020年11月07日08:30--10:30

报告地点：腾讯会议832 517 338

专家简介:教授，硕士生导师，主持省部级科研项目4项、参与国家级项目3项，主持参与省部级教改项目4项，获陕西省自然科学奖二等奖、陕西省高等学校科学技术奖一等奖、陕西省高等教育教学成果奖一等奖。现任《数学评论》评论员，担任《Semigroup Forum》,《Algebra Universalis》等杂志的匿名审稿人。研究方向为半群代数理论。

报告摘要：In this talk we study the semiring variety ${\mathbf V}$ generated by any finite number of finite fields$F_{1},\,\cdots,\, F_{k}$ and two-element distributive lattice $B_2$, i.e., ${\mathbf V}={\mathbf {HSP}} \{B_{2},\,F_{1},\,\cdots,\, F_{k}\}$. Properties and structure of semirings in ${\mathbf V}$ are fully characterized. It is proved that ${\mathbf V}$ is hereditarily finitely based, and that, up to isomorphism, the two-element distributive lattice $B_{2}$ and all subfields of $F_{1},\,\cdots,\, F_{k}$ are the only subdirectly irreducible semirings in ${\mathbf V}$. We further investigate the problem of finite basis of some semiring varieties generated by semirings with finite order.

邀请人：刘合国