Extensions of Unit 1-Stable Range

Abstract

In this paper, we investigate necessary and sufficient conditions under which a ring R satisfies unit ideal–stable range conditions. We prove that if I is a bounded regular ideal of a ring R, then unit (I)-stable range condition, unit ⟨I⟩-stable range condition and unit [I]-stable range condition coincide with each other.

Key Words:

• Unit ideal–stable range
• Matrix extension
• Regular ideal

Mathematics Subject Classification:

• 16U99
• 16E50

Acknowledgment

It is a pleasure to thank the referee for excellent suggestions and corrections which led to the new version.

Notes

^#Communicated by B. Huisgen-Zimmermann.