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Projectively condensed semigroups, generalized completely regular semigroups and projective orthomonoids

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Abstract

The class \( \mathcal{P}\mathcal{C} \) of projectively condensed semigroups is a quasivariety of unary semigroups, the class of projective orthomonoids is a subquasivariety of \( \mathcal{P}\mathcal{C} \). Some well-known classes of generalized completely regular semigroups will be regarded as subquasivarieties of \( \mathcal{P}\mathcal{C} \). We give the structure semilattice composition and the standard representation of projective orthomonoids, and then obtain the structure theorems of various generalized orthogroups.

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References

  1. A. El-Qallali, Structure theory for abundant and related semigroups, Ph. D. Thesis (York, 1980).

  2. J. B. Fountain, Right pp monoids with central idempotents, Semigroup Forum, 13 (1977), 229–237.

    Article  MATH  MathSciNet  Google Scholar 

  3. J. B. Fountain, Abundant semigroups, Proc. London Math. Soc., 44 (1982), 103–129.

    Article  MATH  MathSciNet  Google Scholar 

  4. J. B. Fountain, G. M. S. Gomes and V. Gould, A Munn type representation for a class of E-semiadequate semigroups, J. Algebra, 218 (1999), 693–714.

    Article  MATH  MathSciNet  Google Scholar 

  5. G. M. S. Gomes and V. Gould, Proper weakly left ample semigroups, Internat. J. Algebra Comput., 9 (1999), 721–739.

    Article  MATH  MathSciNet  Google Scholar 

  6. X. J. Guo, K. P. Shum and Y. Q. Guo, Perfect rpp semigroups, Comm. Algebra, 29 (2001), 2447–2459.

    Article  MATH  MathSciNet  Google Scholar 

  7. Y. Q. Guo, K. P. Shum and P. Y. Zhu, The structure of left C-rpp semigroups, Semigroup Forum, 50 (1995), 9–23.

    Article  MATH  MathSciNet  Google Scholar 

  8. Y. He, Some studies on regular and generalized regular semigroups, Ph. D. Thesis (Guangzhou, Zhongshan University, 2002).

    Google Scholar 

  9. Y. He, Y. Q. Guo and K. P. Shum, The construction of orthodox super rpp semigroups, Sci. China, 47 (2004), 552–565.

    Article  MATH  MathSciNet  Google Scholar 

  10. Y. He, Y. Q. Guo and K. P. Shum, Standard representations of orthodox semigroups, Comm Algebra, 33 (2005), 745–761.

    Article  MATH  MathSciNet  Google Scholar 

  11. Y. He, F. Shao, S. Q. Li and W. Gao, On Left C-\( \mathcal{U} \)-liberal Semigroups, Czech. Math. J., 56 (2006), 1085–1108.

    Article  MathSciNet  MATH  Google Scholar 

  12. Y. He and X. Z. You, C-\( \mathcal{P} \)-condensed semigroups and the coset semigroups of groups, submitted.

  13. J. M. Howie, An introduction to semigroup theory, Academic Press (Orlando, 1976).

    MATH  Google Scholar 

  14. M. V. Lawson, Rees Matrix semigroups, Proc. Edinburgh Math. Soc., 33 (1990), 23–37.

    Article  MATH  MathSciNet  Google Scholar 

  15. G. Li, Y. Q. Guo and K. P. Shum, A Rees matrix representation theorem for \( \mathcal{U} \)-semisuperabundant semigroups, Inter. Math. J., 3 (2004), 353–363.

    Google Scholar 

  16. G. Li, Y. Q. Guo and K. P. Shum, Quasi-C-Ehremann semigroups and their subclasses, Semigroup Forum, 70 (2005), 369–390.

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  18. M. Petrich, Lectures in Semigroups, Pitman (New York, 1976).

    Google Scholar 

  19. M. Petrich and N. Reilly, Completely Regular Semigroups, John Wiley & Sons (New York, 1998).

    Google Scholar 

  20. X. M. Ren and K. P. Shum, The structure of superabundant semigroups, Sci. China, 33 (2003), 551–561.

    Google Scholar 

  21. A. H. Sankappanavar, A Course in Universal Algebra, Springer Verlag (New York-Berlin, 1981).

    MATH  Google Scholar 

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Authors and Affiliations

  1. School of Mathematical Sciences, South China Normal University, Guangzhou, Guangdong, 510631, China

    Y. Chen

  2. School of Computer Science, Hunan University of Science and Technology, Xiangtan, Hunan, 411201, China

    Y. He

  3. Faculty of Science, The Chinese University of Hong Kong, Shatin, N. T., Hong Kong, China

    K. P. Shum

Authors
  1. Y. Chen
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  2. Y. He
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  3. K. P. Shum
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Corresponding author

Correspondence to Y. He.

Additional information

Partially supported by the National Natural Science Foundation of China (Grant No. 10771077) and the Natural Science Foundation of Guangdong Province (Grant No. 021073; 06025062).

Partially supported by a grant of Natural Scientific Foundation of Hunan (No. 06JJ2025) and a grant of Scientific Research Foundation of Hunan Education Department (No. 05A014).

Partially supported by a UGC (HK) grant #2060123 (04-05).

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Chen, Y., He, Y. & Shum, K.P. Projectively condensed semigroups, generalized completely regular semigroups and projective orthomonoids. Acta Math Hung 119, 281–305 (2008). https://doi.org/10.1007/s10474-007-7038-x

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  • DOI: https://doi.org/10.1007/s10474-007-7038-x

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