Feebly Baer Rings and Modules

Abstract

A right module M over a ring R is called feebly Baer if, whenever xa = 0 with x ∈ M and a ∈ R, there exists e² = e ∈ 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.

Key Words:

• Feebly Baer ring and module
• Von Neumann regular ring
• p.p. ring and module
• Triangular matrix ring
• polynomial modules

Keywords:

• 2010 Mathematics Subject Classification
• Primary 16E50

ACKNOWLEDGMENTS

The authors are grateful to the referee for valuable comments and suggestions.

Notes

Communicated by T. Albn.