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Regularity of semigroup rings

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Abstract

Sufficient conditions are obtained in order that the semigroup rings of some semigroups be regular. For some inverse, orthodox and completely simple semigroups, the necessary and sufficient conditions for the regularity of the semigroup rings are found.

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References

  1. Clifford, A. H. and G. B. Preston, “The Algebraic Theory of Semigroups”, Vol. I, Amer. Math. Soc., Providence, R.I., 1961.

    MATH  Google Scholar 

  2. Connell, I. G.,On the Group Ring, Canad. J. Math.15 (1963), 650–685.

    MATH  MathSciNet  Google Scholar 

  3. Goodearl, K. R., “Von Neumann Regular Rings”, Pitman, London, 1979.

    MATH  Google Scholar 

  4. Howie, J. M., “An Introduction to Semigroup Theory”, Academic Press, New York, 1976.

    MATH  Google Scholar 

  5. Janeski, J. and J. Weissglass,Regularity of Semilattice Sums of Rings, Proc. Amer. Math. Soc.39 (1973), 479–482.

    Article  MATH  MathSciNet  Google Scholar 

  6. Li, F.,Some Studies on Semigroups and Semigroup Rings, Doctoral Dissertation, Lanzhou University, China, 1991.

    Google Scholar 

  7. Petrich, M., “Inverse Semigroups”, John Wiley & Sons, New York, 1984.

    MATH  Google Scholar 

  8. Ponizovskiî, J. S.,Semigroup Rings, Semigroup Forum36 (1987), 1–46.

    Article  MathSciNet  Google Scholar 

  9. Weissglass, J.,Regularity of Semigroup Rings, Proc. Amer. Math. Soc.25 (1970), 499–503.

    Article  MATH  MathSciNet  Google Scholar 

  10. Wenger, R. H.,Some Semigroups Having Quasi-Frobenius Algebras, I, Proc. London Math. Soc. (3),18 (1968), 484–494.

    Article  MATH  MathSciNet  Google Scholar 

  11. Yamada, M.,Generalized Brandt Semigroups, Mem. Fac. Lit. & Sci., Shimane Univ., Nat. Sci.3 (March 20, 1970), 1–8.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics & Mechanics, Southeast University, Nanjing, 210096, Jiangsu, P.R. China

    Fang Li

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  1. Fang Li
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Additional information

Communicated by J. S. Ponizovskii

The author wishes to thank Prof. Y. Q. Guo for his best help and advice. Key Words and Phrases: (von Neumann) regularity, semigroup ring, inverse semigroup, orthodox semigroup, completely [0-] simple semigroup.

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Li, F. Regularity of semigroup rings. Semigroup Forum 53, 72–81 (1996). https://doi.org/10.1007/BF02574122

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  • DOI: https://doi.org/10.1007/BF02574122

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