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.
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References
Blyth, T.S., Almeida Santos, M.H.: Amenable orders associated with inverse transversals. J. Algebra 240(1), 143–164 (2001)
Blyth, T.S., Almeida Santos, M.H.: On amenable orders and inverse transversals. Commun. Algebra 39(6), 2189–2209 (2011)
Blyth, T.S., Almeida Santos, M.H.: \(\cal H\)-Cohesive order associated with inverse transversals. Commun. Algebra 40(8), 2771–2785 (2012)
Blyth, T.S., McFadden, R.B.: Regular semigroups with a multiplicative inverse transversal. Proc. R. Soc. Edinb. 92A, 253–270 (1982)
Chen, J.F.: On regular semigroups with orthodox transversals. Commun. Algebra 27, 4275–4288 (1999)
Chen, J.F., Guo, Y.Q.: Orthodox transversals of regular semigroups. Int. J. Algebra Comput. 11(2), 269–279 (2001)
Gigon, R.S.: Rectangular group congruences on a semigroup. Semigroup Forum 87(1), 120–128 (2013)
Howie, J.M.: An Introduction to Semigroup Theory. Academic Press, London (1976)
Howie, J.M.: Fundamentals of Semigroup Theory. Clarendon Press, Oxford (1995)
Kong, X.J.: Regular semigroups with quasi-ideal orthodox transversals. Semigroup Forum 74(2), 247–258 (2007)
Kong, X.J.: On generalized orthodox transversals. Commun. Algebra 42(2), 1431–1447 (2014)
Kong, X.J., Luo, Y.F.: Regular semigroups with left simplistic orthodox transversals (in Chinese). Sci. Sin. Math. 41(8), 745–757 (2011)
Kong, X.J., Zhao, X.: A new construction for regular semigroups with quasi-ideal orthodox transversals. J. Aust. Math. Soc. 86(2), 177–187 (2009)
McAlister, D.B., McFadden, R.B.: Regular semigroups with inverse transversals. Q. J. Math. 34(2), 459–474 (1983)
Saito, T.: Construction of regular semigroups with inverse transversals. Proc. Edinb. Math. Soc. 32, 41–51 (1989)
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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Communicated by Marcel Jackson.
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Kong, X., Meng, F. The generalization of two basic results for orthodox semigroups. Semigroup Forum 89, 394–402 (2014). https://doi.org/10.1007/s00233-014-9576-1
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DOI: https://doi.org/10.1007/s00233-014-9576-1