Semigroup Forum

, Volume 12, Issue 1, pp 183–184 | Cite as

Note on the orderability of idempotent semigroups

  • Thérèse Merlier
Short Note


In [3] , we gave a condition for the orderability of finite idempotent semigroups. Recently, in [5], T. Saitô gives a condition for the orderability of idempotent semigroups in the general case. As Corollary ( 4–13 of [5] ), he obtains an idempotent semigroup S is orderable if and only if every finite subsemigroup of S is orderable. The purpose of this note is to give a direct proof of this result.


Direct Proof Idempotent Semigroup 
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Copyright information

© Springer-Verlag New York Inc. 1976

Authors and Affiliations

  • Thérèse Merlier
    • 1
  1. 1.PARIS- Université Pierre et Marie CurieFontenay aux RosesFrance

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