Semigroup Forum

, Volume 3, Issue 1, pp 160–167

Note on exclusive semigroups

  • Miyuki Yamada
Research Announcements

DOI: 10.1007/BF02572956

Cite this article as:
Yamada, M. Semigroup Forum (1971) 3: 160. doi:10.1007/BF02572956


In the SEMIGROUP FORUM, Vol. 1, No. 1, B. M. Schein proposed the following problem:

Describe the structure of semigroups S such that for every a,b,c∈S, abc=ab, bc or ac. At present, we shall call such a semigroup S anexclusivesemigroup. Recently, the author heard that the structure of commutative exclusive semigroups was completely determined by T. Tamura [3]. In this paper, we deal with exclusive semigroups which are not necessarily commutative. The paper is divided into three sections. At first, the structure of exclusive semigroups whose idempotents form a rectangular band will be clarified. Next, we shall investigate a certain class of exclusive semigroups called “exclusive homobands”. Especially, in the final section we shall deal with medial exclusive homobands and show how to construct them. The proofs are omitted and will be given in detail elsewhere.

Copyright information

© Springer-Verlag New York Inc. 1971

Authors and Affiliations

  • Miyuki Yamada
    • 1
  1. 1.Shimane UniversityShimaneJapan

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