Speaker:  Prof. T. Y. Lam

         (University of California, Berkeley)

Title: Jacobson's Lemma and Its Various Extensions

Time:     16:10-17:10pm, Sept. 25, 2012 (Tue.)

Venue:    浙江大学数学研究中心202

Abstract. A well-known lemma of Jacobson states that, if 1-ab is invertible in a ring R, then so is 1-ba. It is natural to seek generalizations of Jacobson's Lemma by asking: if 1-ab∈R has a certain ring-theoretic property (P), when can we say that its Jacobson twin  1-ba also has the same property? Surprisingly,

this question has been effectively considered only in the last decade.

In this talk, we'll briefly report on some of the recent work done in this area, focusing especially on the case where (P) is taken to be the Drazin invertible property, or the strongly clean property.