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All varieties of bands

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Abstract

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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References

  1. KIMURA, N.: Note on idempotent semigroups. IV. Identities of three variables, Proc. Japan Acad.34, 121–123 (1958).

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  2. PETRICH, M.: Topics in semigroups, Lecture Notes, The Pennsylvania State University, 1967.

  3. YAMADA, M.: The structure of separative bands, Doctoral dissertation, University of Utah, 1962.

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Authors and Affiliations

  1. Dept. of Mathematics, The Pennsylvania State University, 16802, University Park, Pennsylvania

    Charles Fennemore

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  1. Charles Fennemore
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Communicated by M. Petrich

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Fennemore, C. All varieties of bands. Semigroup Forum 1, 172–179 (1970). https://doi.org/10.1007/BF02573031

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  • DOI: https://doi.org/10.1007/BF02573031

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