Semigroup Forum

, Volume 1, Issue 1, pp 172–179

All varieties of bands

  • Charles Fennemore
Research Announcements


The object of this paper is to describe the lattice of varieties of bands, and to present some related results. For example, each variety of bands is defined by exactly one identity from a countably infinite set of identities which we state explicitly. Two results concerning bands contained in an arbitrary variety of bands are stated.


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  1. 1.
    KIMURA, N.: Note on idempotent semigroups. IV. Identities of three variables, Proc. Japan Acad.34, 121–123 (1958).MATHCrossRefGoogle Scholar
  2. 2.
    PETRICH, M.: Topics in semigroups, Lecture Notes, The Pennsylvania State University, 1967.Google Scholar
  3. 3.
    YAMADA, M.: The structure of separative bands, Doctoral dissertation, University of Utah, 1962.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1970

Authors and Affiliations

  • Charles Fennemore
    • 1
  1. 1.Dept. of MathematicsThe Pennsylvania State UniversityUniversity Park

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