Abstract
Generalized orthodox transversals are introduced in this article, and some characterizations associated with them are obtained. The related results of Chen on quasi-ideal orthodox transversals obtained in 1999 and Zhang and Wang on generalized inverse transversals obtained in 2008 are generalized and amplified. A structure theorem of a regular semigroup with a perfect generalized orthodox transversal is also established.
2010 Mathematics Subject Classification:
ACKNOWLEDGMENTS
The author would like to express his sincere thanks to Professor Victoria Gould and the referees for their important and constructive modifying suggestions.
The author is a postdoctoral researcher of the Postdoctoral Station of Qufu Normal University. The research is partially supported by China Postdoctoral Science Foundation (2013M541883), RFDP (20133705120002), Science and Technology Project in University of Shandong Province (J13L107), Doctoral Scientific Research Start Foundation of Qufu Normal University, Scientific Research Foundation of Qufu Normal University (XJ201215), Mathematical Tianyuan Foundation of China (No. 11126186), Shandong Provincial NSF (No. ZR2011AM013, ZR2010AL010).
Notes
Communicated by V. Gould.