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Band of t-archimedean semigroups

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Abstract

A semigroup S is called t-archimedean if for all a,b∈S, there exists a positive integer i such that bi∈aS∩Sa. The purpose of this paper is to characterize semigroups which are bands of t-archimedean semigroups. We then apply this result to exponential semigroups.

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References

  1. Clifford, A. H. and G. B. Preston,The Algebraic Theory of Semigroups, Vol. 1, Amer. Math. Soc. Providence, Rhode Island 1961.

    Book  MATH  Google Scholar 

  2. Chrislock, J.,On medial semigroups, J. Algebra 12 (1969), 1–9.

    Article  MathSciNet  MATH  Google Scholar 

  3. Putcha, M. S.,Semilattice decompositions of semigroups, Semigroup Forum 6 (1973), 12–34.

    Article  MathSciNet  MATH  Google Scholar 

  4. Putcha, M. S.,Minimal sequences in semigroups, Trans. Amer. Math. Soc. (to appear).

  5. —,Semigroups in which a power of each element lies in a subgroup, Semigroup Forum 5 (1973), 354–361.

    Article  MathSciNet  MATH  Google Scholar 

  6. Putcha, M. S.Paths in graphs and minimal π-sequences in semigroups (submitted).

  7. Putcha, M. S. and J. Weissglass,Band decompositions of semigroups, Proc. Amer. Math. Soc. 33 (1972), 1–7.

    Article  MathSciNet  MATH  Google Scholar 

  8. Tamura, T.,The theory of construction of finite semigroups I. Osaka Math. J. 8 (1956), 243–261.

    MathSciNet  MATH  Google Scholar 

  9. —,Another proof of a theorem concerning the greatest semilattice decomposition of a semigroup, Proc. Japan Acad. 40 (1964), 777–780.

    Article  MathSciNet  MATH  Google Scholar 

  10. —,On Putcha's theorem concerning semilattice of archimedean semigroups, Semigroup Forum 4 (1972), 83–86.

    Article  MathSciNet  MATH  Google Scholar 

  11. Tamura, T.,Quasi-orders,generalized archimedeaness and semilattice decompositions, to appear.

  12. —,Note on the greatest semilattice decomposition of semigroups, Semigroup Forum 4 (1972), 255–261.

    Article  MathSciNet  MATH  Google Scholar 

  13. Tamura, T.,Semilattice congruences viewed from quasi-orders, to appear.

  14. —,Remark on the smallest semilattice congruence, Semigroup Forum 5 (1973), 277–282.

    Article  MathSciNet  MATH  Google Scholar 

  15. Tamura, T. and N. Kimura,On decomposition of a commutative semigroup, Kodai Math. Sem. Rep. 4 (1954), 109–112.

    Article  MathSciNet  MATH  Google Scholar 

  16. Tamura, T. and J. Shafer,On exponential semigroups I, Proc. Japan Acad. 48 (1972), 77–80.

    Article  MathSciNet  MATH  Google Scholar 

  17. Petrich, M.,Introduction to semigroups, Merill Publishing Company, 1973.

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Authors and Affiliations

  1. Department of Mathematics, University of California, 93106, Santa Barbara, California, USA

    Mohan S. Putcha

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  1. Mohan S. Putcha
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Communicated by M. Petrich

National Science Foundation Fellow

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Putcha, M.S. Band of t-archimedean semigroups. Semigroup Forum 6, 232–239 (1973). https://doi.org/10.1007/BF02389126

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  • DOI: https://doi.org/10.1007/BF02389126

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