In this note, a counterexample is given to show that a noncommutative VNL-ring need not be an SVNL-ring, answering an open question of Chen and Tong （Glasgow Math. J., 48（1）（2006）） negatively. Moreover, some new...In this note, a counterexample is given to show that a noncommutative VNL-ring need not be an SVNL-ring, answering an open question of Chen and Tong （Glasgow Math. J., 48（1）（2006）） negatively. Moreover, some new results about VNL-rings and GVNL-ringsare also given.展开更多
Let R be a ring. An element a of R is called a left PP-element if Ra is projective. The ring R is said to be a left almost PP-ring provided that for any element a of R, either a or 1 - α is left PP. We develop, in th...Let R be a ring. An element a of R is called a left PP-element if Ra is projective. The ring R is said to be a left almost PP-ring provided that for any element a of R, either a or 1 - α is left PP. We develop, in this paper, left almost PP-rings as a generalization of von Neumann local （VNL） rings and left PP-rings. Some properties of left almost PP-rings are studied and some examples are also constructed.展开更多
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
文摘In this note, a counterexample is given to show that a noncommutative VNL-ring need not be an SVNL-ring, answering an open question of Chen and Tong （Glasgow Math. J., 48（1）（2006）） negatively. Moreover, some new results about VNL-rings and GVNL-ringsare also given.
基金Supported by the Natural Science Foundation of Hunan Province(Grant No.2016JJ2050)
文摘Let R be a ring. An element a of R is called a left PP-element if Ra is projective. The ring R is said to be a left almost PP-ring provided that for any element a of R, either a or 1 - α is left PP. We develop, in this paper, left almost PP-rings as a generalization of von Neumann local （VNL） rings and left PP-rings. Some properties of left almost PP-rings are studied and some examples are also constructed.
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.
