Abstract
In the present paper, a series of results and examples that explore the structural features of \(\mathcal {H}\)-commutative semigroups are provided. We also generalize a result of Isbell from commutative semigroups to \(\mathcal {H}\)-commutative semigroups by showing that the dominion of an \(\mathcal {H}\)-commutative semigroup is \(\mathcal {H}\)-commutative. We then use this to generalize Howie and Isbell’s result that any \(\mathcal {H}\)-commutative semigroup satisfying the minimum condition on principal ideals is saturated.
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Acknowledgements
We sincerely thank the learned referee for his useful and constructive suggestions, including that of Theorem 4.10, that helped considerably to improve the presentation of the paper.
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Communicated by Victoria Gould.
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Alam, N., Higgins, P.M. & Khan, N.M. Epimorphisms, dominions and \(\mathcal {H}\)-commutative semigroups. Semigroup Forum 100, 349–363 (2020). https://doi.org/10.1007/s00233-019-10050-z
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DOI: https://doi.org/10.1007/s00233-019-10050-z