Simple-Baer Rings and Minannihilator Modules

Abstract

Let R be a ring. M is said to be a minannihilator left R-module if r _M l _R (I) = IM for any simple right ideal I of R. A right R-module N is called simple-flat if Nl _R (I) = l _N (I) for any simple right ideal I of R. R is said to be a left simple-Baer (resp., left simple-coherent) ring if the left annihilator of every simple right ideal is a direct summand of _R R (resp., finitely generated). We first obtain some properties of minannihilator and simple-flat modules. Then we characterize simple-coherent rings, simple-Baer rings, and universally mininjective rings using minannihilator and simple-flat modules.

Key Words:

• Minannihilator module
• Precover
• Preenvelope
• Simple-Baer ring
• Simple-coherent ring
• Simple-flat module
• Universally mininjective ring

2000 Mathematics Subject Classification:

• 16D40
• 16D50
• 16D60
• 16P70

ACKNOWLEDGMENTS

This research was partially supported by NSFC (11071111, 11171149), NSF of Jiangsu Province of China (BK2011068), Jiangsu 333 Project, Jiangsu Six Major Talents Peak Project. The author would like to thank Professor Toma Albu and the referee for the very helpful comments and suggestions.

Notes

Communicated by T. Albu.