On Hochschild Extensions of Reduced and Clean Rings

Abstract

We show that an arbitrary Hochschild extension of a reduced ring by a two-sided ideal is symmetric and reversible, and that any Hochschild extension of a clean ring by an arbitrary bimodule is clean. This generalizes a result of Kim and Lee, and provides many examples of clean rings.

Key Words:

• Hochschild extension
• Reduced ring
• Reversible ring
• Symmetric ring

2000 Mathematics Subject Classification:

• 16D10
• 16U60
• 16E60

ACKNOWLEDGMENTS

The authors gratefully acknowledge the support from the Research Fund of Doctor Program of Higher Education (20040027002), Ministry of Education of China. The authors thank R. Wisbauer for reading the manuscript. Also, C. C. Xi thanks the Alexander von Humboldt Foundation, Germany, for support.

Notes

Communicated by R. Wisbauer.