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Epimorphisms, dominions and varieties of bands

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Abstract

We show that all subvarieties of left regular bands are closed in the variety of all bands. We also show that all subvarieties of left seminormal bands are saturated in the variety of all bands which shows that, in the category of all bands, any epi from a left seminormal band is surjective.

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Acknowledgements

We sincerely thank the learned referee for his constructive, but critical suggestions that helped us to improve the presentation of the paper. The second author acknowledges the financial support from Science and Engineering Research Board, Govt. of India under the Extra Meural Reseach Grant EMR/2016/007168.

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Authors and Affiliations

  1. Department of Mathematics, Central University of Kashmir, Nowgam, Srinagar, 190015, India

    Shabir Ahmad Ahanger & Aftab Hussain Shah

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  1. Shabir Ahmad Ahanger
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  2. Aftab Hussain Shah
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Correspondence to Shabir Ahmad Ahanger.

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Communicated by Mark V. Lawson.

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Ahanger, S.A., Shah, A.H. Epimorphisms, dominions and varieties of bands. Semigroup Forum 100, 641–650 (2020). https://doi.org/10.1007/s00233-019-10047-8

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  • DOI: https://doi.org/10.1007/s00233-019-10047-8

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