报告题目：Equational theories of certain involutory $\mathscr{J}$--trivial monoids

报 告 人：罗彦锋教授（兰州大学）

报告时间：2026年1月10日（星期六）上午9:30-10:30

报告地点：数学大楼911

参加人员：教师、研究生

报告摘要：Let $BR_n$ be the monoid of all $n\times n$ Boolean matrices with $1$s on the main diagonal. It is known that $BR_n$ can be identified with the monoid of all reflexive binary relations on an $n$-element set under composition. The monoid $BR_n$ admits two natural unary operations: transposition $^T$ and skew transposition $^D$, which make $BR_n$ an involutory monoid. A semigroup is said to be $\mathscr{J}$-trivial if its $\mathscr{J}$-relation is the identity relation. It has been shown that a finite monoid $M$ is $\mathscr{J}$-trivial if and only if $M$ divides the monoid $BR_n$ for some $n$. In this talk, we introduce and study the equational theories of certain $\mathscr{J}$-trivial monoids endowed with involutions, these involutory $\mathscr{J}$-trivial monoids arise mainly as involutory submonoids of $(BR_n, ^T)$ and $(BR_n, ^D)$. We completely resolve the finite basis problems for these monoids and investigate the equational equivalence problem among them.

报告人简介：罗彦锋，兰州大学教授、萃英学者、博士生导师，享受国务院政府特殊津贴。主要从事代数学的人才培养及研究工作，发表学术论文近120篇，主持完成多项国家自然科学基金和省部级科研项目；获甘肃省自然科学二等奖、科技进步三等奖及甘肃省教学成果特等奖各1项；2002年受教育部“重点高校系主任/研究所骨干出国研修计划项目”资助到加拿大西蒙弗雷泽大学访学。编著出版《线性代数》国家级规划教材1部；获甘肃省“高等学校教学名师奖”、宝钢优秀教师奖；曾任教育部普通高等学校数学类专业教学指导委员会委员、中国高等教育学会理科教育专业委员会秘书长、甘肃省数学会副理事长等。