A ring R is called a GVNL-ring if a or 1-a is π-regular for every a∈R,as a common generalization of local and π-regular rings.It is proved that if R is a GVNL ring,then either(1-e)R(1-e) or eRe is a π-regular ring...A ring R is called a GVNL-ring if a or 1-a is π-regular for every a∈R,as a common generalization of local and π-regular rings.It is proved that if R is a GVNL ring,then either(1-e)R(1-e) or eRe is a π-regular ring for every idempotent e of R.We prove that the center of a GVNL ring is also GVNL and every abelian GVNL ring is SGVNL.The formal power series ring R[x] is GVNL if and only if R is a local ring.展开更多
基金supported by the grant of National Natural Science Foundation of China(10971024)the Nanjing University of Posts and Telecommunications(NY209022)
文摘A ring R is called a GVNL-ring if a or 1-a is π-regular for every a∈R,as a common generalization of local and π-regular rings.It is proved that if R is a GVNL ring,then either(1-e)R(1-e) or eRe is a π-regular ring for every idempotent e of R.We prove that the center of a GVNL ring is also GVNL and every abelian GVNL ring is SGVNL.The formal power series ring R[x] is GVNL if and only if R is a local ring.
