Modules with the Beachy–Blair Condition

Abstract

A right R-module satisfies the right Beachy–Blair condition if each of its faithful submodules is cofaithful. In this article we study the relationship between the right Beachy–Blair condition of a right R-module and its skew polynomial, skew monoid and skew generalized power series extensions. Consequently, several known results regarding rings satisfying the right Beachy–Blair condition are extended to a more general setting.

Key Words:

• Beachy–Blair condition
• Skew generalized power series ring
• Skew monoid ring

2010 MR Subject Classification:

• 16D25
• 16S36

ACKNOWLEDGMENTS

We would like to express deep gratitude to the referee for his/her valuable suggestions which improved the presentation of the article. This research is supported by the National Natural Science Foundation of China (10771058, 11071062), Natural Science Foundation of Hunan Province (10jj3065), and Scientific Research Fundation of Hunan Provincial Education Department (10A033).

Notes

Communicated by V. A. Artamonov.