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On exclusive semigroups

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Abstract

The following problem was posed by the second author in ‘Semigroup Forum’, Vol. 1, No. 1, 1970, p. 91:

Describe the structure of semigroups S such that for all a, b, c ε S, abc=ab, ac or bc.

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References

  1. Clifford, A. H. and G. B. Preston,The Algebraic Theory of Semigroups, Vol. 1, Providence, 1961.

  2. Green, J.,On the structure of semi-groups, Ann. Math. (2) 54 (1951), 163–172.

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  4. Tamura, T.,On commutative exclusive semigroups, Semigroup Forum, 2(2), (1971), 181–187.

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  5. Yamada, M.,Note on exclusive semigroups, Semigroup forum, to appear.

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Authors and Affiliations

  1. Northern Illinois University, 60115, DeKalb, Illinois

    L. O’Carroll & B. M. Schein

  2. The Saratov State University, Saratov, U.S.S.R.

    L. O’Carroll & B. M. Schein

Authors
  1. L. O’Carroll
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  2. B. M. Schein
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O’Carroll, L., Schein, B.M. On exclusive semigroups. Semigroup Forum 3, 338–348 (1971). https://doi.org/10.1007/BF02572971

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  • DOI: https://doi.org/10.1007/BF02572971

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