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Varieties Generated by Ordered Bands I

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Abstract

Ordered bands are regarded as semirings whose multiplicative reduct is a band and whose additive reduct is a chain. We find the variety of semirings generated by all ordered bands and we determine part of the lattice of its subvarieties.

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References

  1. Gerhard, J. A. and Petrich, M.: Varieties of bands revisited, Proc. Lond. Math. Soc. 58 (1989), 323–350.

    Article  MATH  MathSciNet  Google Scholar 

  2. Graczynska, E. and Pastijn, F.: Proofs of regular identities, Houst. J. Math. 8 (1982), 61–67.

    MATH  MathSciNet  Google Scholar 

  3. Howie, J. M.: Fundamentals of Semigroup Theory, Oxford Science, Oxford, 1995.

    MATH  Google Scholar 

  4. McKenzie, R. N., McNulty, G. F. and Taylor, W. F.: Algebras, Lattices, Varieties, Vol. 1, Wadsworth Brooks/Cole, Monterey, 1987.

    Google Scholar 

  5. McKenzie, R. N. and Romanowska, A.: Varieties of ·-distributive bisemilattices, in Contributions to General Algebra (Proc. Klagenfurt Conf., Klagenfurt, 1978), Heyn, Klagenfurt, 1979; pp. 213–218.

  6. Pastijn, F.: Idempotent distributive semirings II, Semigroup Forum 26 (1983), 153–166.

    Article  MathSciNet  Google Scholar 

  7. Pastijn, F. and Guo, Y. Q.: The lattice of idempotent distributive semiring varieties, Science in China (Ser. A) 42 (1999), 785–804.

    Article  MATH  MathSciNet  Google Scholar 

  8. Pastijn, F. and Romanowska, A.: Idempotent distributive semirings, Acta Sci. Math. (Szeged) 44 (1982), 239–253.

    MATH  MathSciNet  Google Scholar 

  9. Pastijn, F. and Zhao, X. Z.: Green's \({\user1{\mathcal{D}}}\)-relation for the multiplicative reduct of an idempotent semiring, Arch. Math. (Brno) 36 (2000), 77–93.

    MATH  MathSciNet  Google Scholar 

  10. Pastijn, F. and Zhao, X. Z.: Varieties of idempotent semirings with commutative addition, Algebra Univers., to appear.

  11. Petrich, M.: Lectures in Semigroups, Wiley, London, 1977.

    Google Scholar 

  12. Płonka, J.: On a method of construction of abstract algebras, Fundam. Math. 61 (1967), 183–189.

    MATH  Google Scholar 

  13. Saitô, T.: Ordered idempotent semigroups, J. Math. Soc. Jpn. 14 (1962), 150–169.

    Article  MATH  Google Scholar 

  14. Saitô, T.: The orderability of idempotent semigroups, Semigroup Forum 7 (1974), 264–285.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Jadavpur University, Kolkata, 700032, India

    S. Ghosh

  2. Department of Mathematics, Statistics, and Computer Science, Marquette University, P.O. Box 1881, Milwaukee,, WI, 53201-1881, USA

    F. Pastijn

  3. Department of Mathematics, Northwest University, Shaanxi Xi’an, 710069, PR China

    X. Z. Zhao

Authors
  1. S. Ghosh
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  2. F. Pastijn
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  3. X. Z. Zhao
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Correspondence to F. Pastijn.

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Ghosh, S., Pastijn, F. & Zhao, X.Z. Varieties Generated by Ordered Bands I. Order 22, 109–128 (2005). https://doi.org/10.1007/s11083-005-9011-z

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  • DOI: https://doi.org/10.1007/s11083-005-9011-z

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