形式三角矩阵环的Quasi-morphic性(英文)

The Quasi-morphic Property of Formal Triangular Matrix Ring

环R称为左Quasi-morphic环,是指对任意a∈R都存在b,c∈R使得Ra=l(b)并且l(a)=Rc。文章主要证明了:BMA的形式三角矩阵环T={(ma 0b):a∈A,b∈B,m∈M}是Quasi-morphic当且仅当A,B是Quasi-morphic并且M=0。这个结果引导我们研究了Quasi-morphic环的corner环的Quasi-morphic性。

A ring is called left quasi - morphic, if for each a∈ R, there exist b and c in R such that Ra = l（b） and l（a） Rc. The main theorem of this paper is that, the formal triangular matrix rings T={（mb,a0）a∈A：b∈B,m∈A} M of （B,A） -bimoduleMis quasi - morphic if and only ifA, B is quasi -morphic and M = 0. This leads to investigate the quasi - morphic property of comer ring R, where R is a quasi - morphic ring.