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Pseudo-C-rpp semigroups

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Abstract

The aim of this paper is to study a class of right pp semigroups, so-called pseudo-C-rpp semigroups. After obtaining some characterizations of pseudo-C-rpp semigroups, we establish a construction of such semigroups in terms of left normal bands and right C-rpp semigroups. In particular, a special case is considered.

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References

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

    Article  MATH  MathSciNet  Google Scholar 

  2. Fountain, J. B.: Right pp momids with central idempotents. Semigroup Forum, 13, 9–23 (1977)

    Google Scholar 

  3. Guo, X. J., Guo, Y. Q., Shum, K. P.: Left abundant semigroups. Communications in Algebra, 32, 2061–2085 (2004)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  5. Guo, X. J.: The structure of PI-strongly rpp semigroups. Chinese Science Bulletin, 41, 1647–1650 (1996)

    Google Scholar 

  6. Guo, X. J.: The structure of Nbe-rpp semigroups. Northeastern Math. J., 16, 398–404 (2000)

    MATH  Google Scholar 

  7. Guo, X. J., Guo, Y. Q.: The translational hull on a strongly right type-A semigroup. Sci. China, Ser. A, 29, 1002–1008 (2000)

    Google Scholar 

  8. Guo, X. J., Guo, Y. Q., Shum, K. P.: Semispined product structure of left C-a semigroups. In: Semigroups (ed: K.P. Shum, Y.Q. Guo et al.), Springer-Verlag, Singapore, 157–166 (1998)

    Google Scholar 

  9. Guo, X. J., Ren, C. C., Shum, K. P.: Dual wreath product structure of right C-rpp semigroups. Algebra Colloquium, 14, 285–294 (2007)

    MATH  MathSciNet  Google Scholar 

  10. Guo, X. J., Shum, K. P.: On left cyber groups. Inter. Math. J., 5, 705–717 (2004)

    MATH  MathSciNet  Google Scholar 

  11. Guo, X. J., Shum, K. P., Guo, Y. Q.: Perfect rpp semigroups. Communications in Algebra, 29, 2447–2460 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  12. Guo, Y. Q.: On the dual of left C-rpp semigroups. Chinese Science Bulletin, 42, 1599–1603 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  13. Guo, Y. Q., Ren, X. M., Shum, K. P.: Another structure of left C-semigroups. Advances in Mathematics (China), 24(1), 39–43 (1995)

    MATH  MathSciNet  Google Scholar 

  14. Shum, K. P., Guo, X. J., Ren, X. M.: (ℓ)-Green’s relations and perfect rpp semigroups. In: Proceedings of the 3th Asian Mathematical Conference 2000 (ed: T. Sunada, W.S. Polly and L. Yang), 604–613

  15. Shum, K. P., Ren, X. M.: The structure of right C-rpp semigroups. Semigroup Forum, 68, 280–292 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  16. Guo, X. J., Wu, A. J.: A note on left C-rpp semigroups. J. Jiangxi Normal Univ. (Natural Sci.), 29, 283–286 (2005)

    MATH  MathSciNet  Google Scholar 

  17. Guo, X. J., Zhao, M., Shum, K. P.: Wreath product structure of left C-rpp semigroups. Algebra Colloquium, 15, 101–108 (2008)

    MATH  MathSciNet  Google Scholar 

  18. Howie, J. M.: An Introduction to Semigroup Theory, Academic Press, London, 1976

    MATH  Google Scholar 

  19. Petrich, M.: Lecture in Semigroups, Akademic Verlag, Berlin, 1977

    Google Scholar 

  20. Guo, Y. Q.: Weakly left C-semigroups. Chinese Science Bull., 41, 462–467 (1996)

    MATH  Google Scholar 

  21. Guo, Y. Q., Shum, K. P., Zhu, P. Y.: On quasi-C-semigroups and some special subclasses. Algebra Colloquium, 6, 105–120 (1999)

    MATH  MathSciNet  Google Scholar 

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Correspondence to Xiao Jiang Guo.

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Supported by the NSF of Jiangxi Province, the SF of Education Department of Jiangxi Province and the SF of Jiangxi Normal University

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Guo, X.J., Jun, Y.B. & Zhao, M. Pseudo-C-rpp semigroups. Acta. Math. Sin.-English Ser. 26, 629–646 (2010). https://doi.org/10.1007/s10114-010-8030-x

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  • DOI: https://doi.org/10.1007/s10114-010-8030-x

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