Feebly Baer Rings and Modules.

A right moduleMover a ringRis called feebly Baer if, wheneverxa = 0 withx ∈ Manda ∈ R, there exists e2 = e ∈ Rsuch that xe = 0 and ea = a. The ringRis called feebly Baer if RRis 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. [ABSTRACT FROM AUTHOR]