Abstract
It has been shown that, for a compact totally ordered set X, the category of irreducible semigroups with idempotents X and idempotent separating homomorphisms has a generator, Irr(X) [7]. In this article we outline the proof of the existence of Irr(X), along with the results obtained previously about the existence of Irr(X). We also survey the known results about the structure of an Irr(X) and about its uniqueness. These latter results were obtained by K. H. Hofmann and the author in a seminar on compact semigroups at Tulane University during the academic year 1970–1971.
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References
Bowman, Thomas T.:A construction principle and compact Clifford semigroups, Semigroup Forum 2(1971), 343–353.
Dauns, John and Karl H. Hofmann:Representations of Rings by Sections, Memoirs of the Amer. Math. Soc. 83 (1968), 180pp.
Hofmann, Karl H. and Paul S. Mostert:Elements of Compact Semigroups, Charles Merrill, Columbus (1966).
Hunter, Robert P.:On the structure of homogroups with applications to the theory of compact connected semigroups, Fund. Math. 52(1963), 62–102.
Hunter, Robert P. and Neal J. Rothman:Characters and cross-sections for certain semigroups, Duke Math. J. 29(1962), 347–366.
Mislove, Michael W.:The existence of Irr(X), Semigroup Forum 1(1970), (Research Announcement),243–248.
Mislove, Michael W.:The existence of Irr(X), submitted to Trans. Amer. Math. Soc.
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Supported by NSF Grant GP28655.
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Mislove, M.W. The existence and structure of Irr(X). Semigroup Forum 4, 1–33 (1972). https://doi.org/10.1007/BF02570766
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DOI: https://doi.org/10.1007/BF02570766