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Abstract
Rowen showed that the 2 by 2 full matrix rings over strongly π-regular rings need not be strongly π-regular. In this note we extend Rowen's method to the n by n full matrix rings. Moreover we show that the n by n full matrix rings over π-regular rings need not be π-regular.
ACKNOWLEDGMENTS
The authors thank the referee for his/her very careful reading of the manuscript and valuable suggestions that improved the article. The first named author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science, and Technology (2010-0021847). The second named author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science, and Technology (2010-0008866).
Notes
Communicated by T. Albu.