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Semigroup Forum

, Volume 89, Issue 2, pp 394–402 | Cite as

The generalization of two basic results for orthodox semigroups

  • Xiangjun Kong
  • Fanwei Meng
Research Article

Abstract

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.

Keywords

Regular semigroup Orthodox semigroup Orthodox transversal Maximum idempotent-separating congruence 

Notes

Acknowledgments

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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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.School of Mathematical SciencesQufu Normal UniversityQufu People’s Republic of China

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