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A class of congruences on a posemigroup

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Abstract

V-completions of partially ordered algebraic systems have been studied by many authors, see Jaffard [7]. In particular, Burgess and McFadden [3] considered V-completions of posemigroups by means of ideal systems.

In seemingly unrelated work, McFadden [10] characterized certain what we shall call ‘strongly isotone’ m-homomorphisms on posemi-groups; while Bigard [1], Dubreil-Jacotin [6] and McFadden [11] studied group homomorphisms on posemigroups.

By determining certain coreflections [8], we prove that any surjective isotone homomorphism on a posemigroup can be factored into an injective strongly isotone homomorphism followed by a surjective strongly isotone m-homorphism. This result is used to bring the previous theories together and to generalise them.

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References

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Authors and Affiliations

  1. Northern Illinois University, 60115, DeKalb, Il

    L. O’Carroll

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  1. L. O’Carroll
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Communicated by A. H. Clifford

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O’Carroll, L. A class of congruences on a posemigroup. Semigroup Forum 3, 173–179 (1971). https://doi.org/10.1007/BF02572958

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  • DOI: https://doi.org/10.1007/BF02572958

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