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This work forms a part of the author's dissertation written under the direction of Professor J. H. Carruth.
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Hays, T.E. Irreducible semigroups are monotone. Semigroup Forum 10, 25–31 (1975). https://doi.org/10.1007/BF02194869
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DOI: https://doi.org/10.1007/BF02194869