FEEBLY BAER RINGS AND MODULES

A right module M over a ring R is called feebly Baer if, whenever xa = 0 with x is an element of M and a is an element of R, there exists e(2) = e is an element of R such that xe = 0 and ea = a. The ring R is called feebly Baer if R-R is a feebly Baer module. These notions are motivated by the commutative analog discussed in a recent paper by Knox, Levy, McGovern, and Shapiro [6]. Basic properties of feebly Baer rings and modules are proved, and their connections with von Neumann regular rings are addressed.