(b,c)-逆的相对性质

Relative Properties of(b,c)-Inverses

研究了相对于一个给定元素d的(b,c)-逆的性质.在更一般的情形下,定义了两类新的广义逆,即左和右(b_(d),c_(d))-逆.证明了右(b_(d),c_(d))-逆是(b,c)-逆的一个新子类,并通过例子说明(b,c)-可逆元未必是右(b_(d),c_(d))-可逆的.研究了右(b_(d),c_(d))-逆上的各种性质,包括Jacobson引理、Cline公式和缠绕性质等.作为应用,利用右(b_(d),c_(d))-逆对abelian环给出了新刻画.

The relative properties of(b,c)-inverses are studied with respect to a given element d in a ring R.The new concepts of left and right(b_(d),c_(d))-inverses are introduced in a more general setting.It’s shown that the class of right(b_(d),c_(d))-inverses is a new subclass of(b,c)-inverses,and an example is given to show that(b,c)-invertible elements need not be right(b_(d),c_(d))-invertible.Various properties including Jacobson’s lemma,Cline’s formula and the intertwining property for right (b_(d),c_(d))-invertible elements are studied.As applications,a new characterization of abelian rings from the point of view of right(b_(d),c_(d))-inverses is given.