报告名称:Semiring varieties generated by finite fields and distributive lattices
主办单位:永利集团88304官网
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、陕西省高等公司产品成果奖一等奖。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