Zero Divisors in Skew Power Series Rings

Abstract

We study the rigid property of rings in the concrete, via power series rings, matrix rings, and Insertion-of-Factors-Property. In the procedure, we concentrate our attention on the skew power-serieswise Armendariz property. We next apply the McCoy condition to skew power series rings, which induces a generalization of skew power-serieswise Armendariz. The relationship is investigated among the properties above and related ring properties, and several known results are obtained as consequences of our results.

Key Words:

• Rigid ring
• Skew Armendariz property
• Skew McCoy condition
• Skew triangular matrix ring

2010 Mathematics Subject Classification:

• 16S36
• 16W20
• 16U80

ACKNOWLEDGMENTS

The authors would like to express their deep gratitude to the referee for a very careful reading of the paper, and many valuable comments, which have greatly improved the presentation of the article.

Notes

Communicated by Q. Wu