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Free product on semihypergroups

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Abstract

In a previous paper [1], we initiated a systematic study of semihypergroups and had a thorough discussion about some important analytic and algebraic objects associated to this class of objects. In this paper, we investigate free structures on the category of semihypergroups. We show that the natural free product structure along with the natural topology, although fails to give a free product for topological groups, works well on a vast non-trivial class of ‘pure’ semihypergroups containing most of the well-known examples including non-trivial coset and orbit spaces.

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Acknowledgements

The author would like to sincerely thank her doctoral thesis advisor Dr. Anthony To-Ming Lau, for suggesting the topic of this study and for the helpful discussions during the course of this work. She is also grateful to the referee for the valuable comments and suggestions.

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  1. Choiti Bandyopadhyay

    Present address: Department of Mathematics, Indian Institute of Technology, Kanpur, India

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  1. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, Canada

    Choiti Bandyopadhyay

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  1. Choiti Bandyopadhyay
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Correspondence to Choiti Bandyopadhyay.

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Communicated by Jimmie D. Lawson.

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This work is part of the author’s Ph.D thesis at the University of Alberta, Canada.

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Bandyopadhyay, C. Free product on semihypergroups. Semigroup Forum 102, 28–47 (2021). https://doi.org/10.1007/s00233-020-10152-z

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