Leavitt path algebras are Bezout

Thời gian: 09:30 đến 11:00 Ngày 15/05/2018

Địa điểm: C2-714, VIASM

Báo cáo viên: Gene Abrams

Tóm tắt:

A ring $R$ is called {\it left B\'{e}zout } in case every finitely generated left ideal of $R$ is principal;  that is, in case for every finite set of elements $\{x_1, x_2, \cdots , x_n\}$ of $R$ there exists $c\in R$ with $\sum_{i=1}^n Rx_i = Rc.$ This property of rings has been studied for many decades.  In this talk we will  describe some of the important aspects of  the proof of the fact that every Leavitt path algebra $L_K(E)$ is left (and right) B\'{e}zout. A central role in the proof is played by a recent result of the speaker with T.G. Nam and N.T. Phuc, namely, a description of the graphs $E$ for which $L_K(E)$ has the so-called Unbounded Generating  Number property. (This is joint work with F. Mantese and A. Tonolo)