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Green's relations in finite function semigroups

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Abstract

Letℱ n be the set of all partial functions on ann-element setX n , i.e., the set of all functions whose domain and range are subsets ofX n . Green's equivalence relationsℛ, ℒ, ℋ andℋ are considered, and the number and cardinality of the corresponding equivalence classes are determined. The number of idempotent and generalized idempotent elements inℱ n is also determined.

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References

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Authors and Affiliations

  1. Massachusetts General Hospital, Boston, Massachusetts, USA

    John Baillieul

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  1. John Baillieul
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I wish to express my gratitude to Professor B. Schweizer for his assistance in the preparation of this manuscript. It is an outgrowth of my senior honors thesis written under his direction at the University of Massachusetts in 1967. My thanks also go to Professor A. Sklar of the Illinois Institute of Technology who suggested a number of improvements in the original manuscript.

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Baillieul, J. Green's relations in finite function semigroups. Aeq. Math. 7, 22–27 (1971). https://doi.org/10.1007/BF01818689

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  • DOI: https://doi.org/10.1007/BF01818689

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