Quasipolar Triangular Matrix Rings Over Local Rings

Abstract

A ring R is quasipolar if for any a ∈ R, there exists p ² = p ∈ R such that , a + p ∈ U(R) and ap ∈ R ^qnil . In this article, we investigate conditions on a local ring R that imply every n × n upper triangular matrix ring over R is quasipolar. It is shown that this is the case for commutative local rings, as well as for a host of other classes of local rings.

Key Words:

• Local ring
• Quasipolar ring
• Strongly clean ring
• Triangular matrix ring

2000 Mathematics Subject Classification:

• 16U99
• 16S99
• 15A09

ACKNOWLEDGMENTS

The authors are highly grateful to the referee for correcting many errors and valuable suggestions. This research is supported by the National Natural Science Foundation of China (10871042, 10971024) and the Specialized Research Fund for the Doctoral Program of Higher Education (200802860024).

Notes

Communicated by S. Sehgal.