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On ℘-regular semigroups having regular *-transversals

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Abstract

Our aim is to investigate the properties and structure of the ℘-regular semigroups having regular *-transversals. We first give two kinds of definitions for regular *-transversals and prove that they are equivalent. A condition for two regular *-transversals of a ℘-regular semigroup to be isomorphic is given. The *-congruences on the ℘-regular semigroups having regular *-transversals are characterized by using the *-congruence triples. In particular, we describe the idempotent separating congruences and the group congruences on such ℘-regular semigroups.

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References

  1. Blyth, T.S., McFadden, R.B.: Regular semigroups with a multiplicative inverse transversal. Proc. R. Soc. Edinb. 92(A), 253–270 (1982)

    MathSciNet  MATH  Google Scholar 

  2. Blyth, T.S., Chen, J.F.: All inverse transversals are mutually isomorphic. Commun. Algebra 29(2), 799–804 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  3. Chen, J.F.: Regular semigroups with orthodox transversals. Commun. Algebra 29(8), 4275–4288 (1999)

    Google Scholar 

  4. Guo, X.J.: Abundant semigroups with a multiplicative adequate transversal. ACTA Math. Sin. Engl. Ser. 18(2), 229–244 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  5. Howie, J.M.: An Introduction to Semigroup Theory. Academic Press, San Diego (1976)

    MATH  Google Scholar 

  6. Li, Y.H.: A class of semigroups with regular *-transversals. Semigroup Forum 65, 43–57 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  7. Nordahl, T.E., Scheiblich, H.E.: Regular *-semigroups. Semigroup Forum 16, 369–377 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  8. Saito, T.: A construction of regular semigroups with inverse transversals. Proc. Edinb. Math. Soc. 32, 41–51 (1989)

    Article  MATH  Google Scholar 

  9. Wang, L.M., Tang, X.L.: Representation of congruences on regular semigroups with inverse transversals. Acta Math. Sin. 41(6), 1159–1164 (1998) (in Chinese)

    MATH  MathSciNet  Google Scholar 

  10. Yamada, M.: ℘-systems in regular semigroups. Semigroup Forum 24, 173–178 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  11. Yamada, M., Sen, M.K.: ℘-regular semigroups. Semigroup Forum 39, 157–178 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  12. Zhang, R.H.: The weakly ℘-regular semigroups and its generalizations. D. Phil. Thesis, Univ. Sichuan (1997)

  13. Zhang, R.H.: The construction of a class of ℘-regular semigroups. J. Pure Math. 15, 23–44 (1998)

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Yunnan Normal University, Kunming, Yunnan, 650092, People’s Republic of China

    Wang Shoufeng

  2. Department of Mathematics, Yuxi Teachers College, Yuxi, Yunnan, 653100, People’s Republic of China

    Yun Liu

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  1. Wang Shoufeng
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  2. Yun Liu
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Correspondence to Wang Shoufeng.

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Communicated by Thomas E. Hall.

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Shoufeng, W., Liu, Y. On ℘-regular semigroups having regular *-transversals. Semigroup Forum 76, 561–575 (2008). https://doi.org/10.1007/s00233-008-9056-6

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  • DOI: https://doi.org/10.1007/s00233-008-9056-6

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