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Congruences on Regular Semigroups with Q-Inverse Transversals

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Ukrainian Mathematical Journal Aims and scope

We present congruences on a regular semigroup with Q-inverse transversal S o by the congruence pair (abstractly), which consists of congruences on the structural component parts R and Λ. It is proved that the set of all congruences for this kind of semigroups is a complete lattice.

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References

  1. T. S. Blyth and R. B. McFadden, “Regular semigroups with a multiplicative inverse transversal,” Proc. Roy. Soc. Edinburgh A, 92, 253–270 (1982).

    Article  MathSciNet  MATH  Google Scholar 

  2. X. L. Tang, “Regular semigroups with inverse transversals,” Semigroup Forum, 55, No. 1, 24–32 (1997).

    Article  MathSciNet  MATH  Google Scholar 

  3. D. B. McAlister and R. B. McFadden, “Regular semigroups with inverse transversals,” Quart. J. Math. Oxford, 34, No. 2, 459–474 (1983).

    Article  MathSciNet  MATH  Google Scholar 

  4. D. B. McAlister and R. B. McFadden, “Regular semigroups with inverse transversals as matrix semigroups,” Quart. J. Math. Oxford, 35, No. 2, 455–474 (1984).

    Article  MathSciNet  MATH  Google Scholar 

  5. L. M. Wang, “On congruence lattice of regular semigroups with Q-inverse transversals,” Semigroup Forum, 50, 141–160 (1995).

    Article  MathSciNet  MATH  Google Scholar 

  6. T. Saito, “Structure of regular semigroups with a quasi-ideal inverse transversals,” Semigroup Forum, 31, 305–309 (1985).

    Article  MathSciNet  MATH  Google Scholar 

  7. M. Petrich, “The structure of completely regular semigroups,” Trans. Amer. Math. Soc., 189, 211–236 (1974).

    Article  MathSciNet  MATH  Google Scholar 

  8. M. Petrich and N. Reilly, Completely Regular Semigroups, Wiley, New York (1999).

    MATH  Google Scholar 

  9. X. L. Tang and L. M.Wang, “Congruences on regular semigroups with inverse transversals,” Comm. Algebra, 23, 4157–4171 (1995).

    Article  MathSciNet  MATH  Google Scholar 

  10. L. M. Wang and X. L. Tang, “Congruence lattices of regular semigroups with inverse transversals,” Comm. Algebra, 26, 1234–1255 (1998).

    MathSciNet  Google Scholar 

  11. T. Saito, “A note on regular semigroups with inverse transversals,” Semigroup Forum, 33, 149–152 (1986).

    Article  MathSciNet  MATH  Google Scholar 

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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, No. 6, pp. 853–859, June, 2016.

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Wang, A., Wang, L. Congruences on Regular Semigroups with Q-Inverse Transversals. Ukr Math J 68, 972–980 (2016). https://doi.org/10.1007/s11253-016-1270-x

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  • DOI: https://doi.org/10.1007/s11253-016-1270-x

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