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Generalized Green's theories

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Abstract

A generalization is given of the relations and equivalences on a semigroup S associated with J. A. Green by introducing the concepts of Green's pairs and generalized Green's theories first on an arbitrary set X and finally on a semigroup S. Most of the results about the usual Green's relations and equivalences are proved, and it is shown that previous generalizations obtained by Wallace, Anscombre, Marki and Steinfeld, and Pastijn may be obtained as special cases of the theory developed.

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Authors and Affiliations

  1. University of Tennessee, 37916, Knoxville, Tennessee

    C. E. Clark & J. H. Carruth

Authors
  1. C. E. Clark
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  2. J. H. Carruth
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Additional information

Communicated by A. H. Clifford

Dedicated to D. D. Miller in honor of his retirement at the University of Tennessee after 32 years of service.

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Clark, C.E., Carruth, J.H. Generalized Green's theories. Semigroup Forum 20, 95–127 (1980). https://doi.org/10.1007/BF02572674

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