The generalization of two basic results for orthodox semigroups
A characterization of orthodox transversals is given and the maximum idempotent-separating congruence concerned with quasi-ideal orthodox transversals is explored. The well-known results about orthodox semigroups are generalized and enriched.
KeywordsRegular semigroup Orthodox semigroup Orthodox transversal Maximum idempotent-separating congruence
The authors would like to express their sincere thanks to M. Jackson and the referees for valuable suggestions and corrections. The first author is a postdoctoral researcher of the Postdoctoral Station of Qufu Normal University. The research is partially supported by the National Natural Science Foundation of China (11171178), the Program for Scientific Research Innovation Team in Colleges and Universities of Shandong Province, Research Fund for the Doctoral Program of Higher Education of China (20133705120002), China Postdoctoral Science Foundation (2013M541883), Shandong Province Postdoctoral Innovation Fund (201303075), A Project of Shandong Province Higher Educational Science and Technology Program (J13LI07), Doctoral Scientific Research Start Foundation of Qufu Normal University (20110129) and Scientific Research Foundation of Qufu Normal University (XJ201215).
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