报告题目: The group of automorphisms of the algebra of one-sided inverses
of a polynomial algebra
报告人：Professor Vladimir Bavula (Universiyt of Sheffield, UK)
报告时间：2018年5月18日14:00-15:00
报告地点：数学楼二楼学术报告厅
摘要: The algebra S(n) of one-sided inverses of the polynomial
algebra P(n) in n variables is obtained from the polynomial algebra
P(n) by adding one-sided (but not two-sided) inverses of its canonical
generators. The algebra S(n) is a non-commutative, non-Noetherian
algebra which is not a domain. It is canonically isomorphic to the
algebra of scalar integro-differential operators.
It has properties that are mixture of properties of the polynomial
algebra P(n) and the Weyl algebra A(n).
Properties of the algebra S(n) will be explained and a set of explicit
generators of its group of automorphisms will be given. The structure
of the automorphism group of S(n) will be discussed.
报告题目: Localizable and weakly left localizable rings
报告人：Professor Vladimir Bavula (Universiyt of Sheffield, UK)
报告地点 2018年5月18日15:00-16:00
报告地点：数学楼二楼学术报告厅
摘要: Two new classes of rings are introduced - the class of left
localizable and the class of weakly left localizable rings. These are
huge classes of rings.
Characterizations of them are given.
报告题目: Generalized Schur's Theorem
报告人：Professor Kaiming Zhao (Wilfrid Laurier University, Canada)
报告地点 2018年5月18日16:00-17:00
报告地点：数学楼二楼学术报告厅
摘要: More than 100 years ago, Schur proved that the maximal dimension of abelian subalgebras of the n by n matrix algebra is $/frac{n^2}{4}+1$ if $n$ is even, and $(n+1)(n-1)/4+1$ if $n$ is odd. I will give a generalization of this theorem.