On Some Artinian QF-3 Rings

Abstract

Carl Faith in 2003 introduced and investigated an interesting class of rings over which every cyclic right module has Σ-injective injective hull (abbr., right CSI-rings) [5]. Inspired by this we investigate rings over which every cyclic right R-module has a projective Σ-injective injective hull. We show that a ring R satisfies this condition if and only if R is right artinian, the injective hull of R _R is projective and every simple right R-module is embedded in R _R . We also characterize right artinian rings in terms of injective faithful right ideals and right CSI-rings.

Key Words:

• Artinian
• CSE-ring
• CSI-ring
• Extending module
• Injective module
• Noetherian ring

2010 Mathematics Subject Classification:

• 16P20
• 16L60
• 16D50
• 16P40

Notes

Communicated by T. Albu.