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Radicals of some semigroup algebras

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Abstract

In this paper we seek to determine the Jacobson radical of certain algebras based on semigroups, and in particular on the semigroups (βS,□), where S is a cancellative, countable, abelian semigroup and βS is its Stone–Čech semigroup compactification. In particular, we wish to determine the radical of ℓ  1(βℕ).

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References

  1. Dales, H.G.: Banach Algebras and Automatic Continuity. London Math. Society Monographs, vol. 24. Clarendon Press, Oxford (2000)

    MATH  Google Scholar 

  2. Dales, H.G., Lau, A.T.-M., Strauss, D.: Banach algebras on semigroups and on their compactifications. Mem. Am. Math. Soc. 205, 1–165 (2010)

    MathSciNet  Google Scholar 

  3. Dales, H.G., Lau, A.T.-M., Strauss, D.: Second duals of measure algebras. Diss. Math. 481, 1–121 (2012)

    MathSciNet  Google Scholar 

  4. Dixon, P.G.: Topologically irreducible representations and radicals in Banach algebras. Proc. Lond. Math. Soc. (3) 74, 174–200 (1997)

    Article  MATH  Google Scholar 

  5. Granirer, E.E.: The radical of L ∞(G)∗. Proc. Am. Math. Soc. 41, 321–324 (1973)

    MathSciNet  MATH  Google Scholar 

  6. Hewitt, E., Zuckerman, H.S.: The ℓ 1-algebra of a commutative semigroup. Trans. Am. Math. Soc. 83, 70–97 (1956)

    MathSciNet  MATH  Google Scholar 

  7. Hindman, N., Pym, J.: Free groups and semigroup in βℕ. Semigroup Forum 30, 177–193 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  8. Hindman, N., Strauss, D.: Algebra in the Stone–Čech Compactification. Theory and Applications. Walter de Gruyter, Berlin (1998). 2nd revised and extended edition (2012)

    Book  MATH  Google Scholar 

  9. Howie, J.M.: Fundamentals of Semigroup Theory. London Mathematical Society Monographs, vol. 12. Clarendon Press, Oxford (1995)

    MATH  Google Scholar 

  10. Malcev, A.: On the immersion of an algebraic ring into a field. Math. Ann. 113, 686–691 (1937)

    Article  MathSciNet  Google Scholar 

  11. Okniński, J.: Semigroup Algebras. Marcel Dekker, New York (1991)

    Google Scholar 

  12. Passman, D.S.: The Algebraic Structure of Group Rings. Wiley, New York (1977)

    MATH  Google Scholar 

  13. Paterson, A.L.T.: Amenability. Mathematical Surveys and Monographs, vol. 29. American Mathematical Society, Providence (1988)

    MATH  Google Scholar 

  14. Zelenyuk, Y.: On subsemigroups of βℕ and absolute coretracts. Semigroup Forum 126, 457–465 (2001)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Fylde College, University of Lancaster, Lancaster, LA1 4YF, UK

    H. Garth Dales

  2. School of Mathematics, University of Leeds, Leeds, LS2 9JT, UK

    Dona E. Strauss

  3. School of Mathematics, University of Witwatersrand, Wits, 2050, Johannesburg, South Africa

    Yevhen Zelenyuk & Yuliya Zelenyuk

Authors
  1. H. Garth Dales
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  2. Dona E. Strauss
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  3. Yevhen Zelenyuk
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  4. Yuliya Zelenyuk
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Corresponding author

Correspondence to H. Garth Dales.

Additional information

Communicated by Jimmie D. Lawson.

This research was commenced when the first and second authors were invited to visit the University of Witwatersrand in December, 2011. They are very grateful for the generous hospitality received.

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Dales, H.G., Strauss, D.E., Zelenyuk, Y. et al. Radicals of some semigroup algebras. Semigroup Forum 87, 80–96 (2013). https://doi.org/10.1007/s00233-012-9459-2

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  • DOI: https://doi.org/10.1007/s00233-012-9459-2

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