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Normal forms for semigroup amalgams

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Abstract

We define a class of inverse semigroup amalgams and derive normal forms for the amalgamated free products in the variety of semigroups. The class includes all amalgams of finite inverse semigroups, recently studied by Cherubini, Jajcayova, Meakin, Nuccio, Piochi and Rodaro (2005–2014), and lower bounded amalgams, that were introduced by the author (1997). We provide sufficient conditions for decidable word problem. We show that the word problem is decidable for an amalgamated free product of finite inverse semigroups. The normal forms can be used to study amalgams in subvarieties of inverse semigroups. In a forthcoming paper by the author, the results are used for varieties of semilattices of groups.

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Authors and Affiliations

  1. 9 Bukit Batok Central Link, The Jade, 21-03, Singapore, 658074, Singapore

    Paul Bennett

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  1. Paul Bennett
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Correspondence to Paul Bennett.

Additional information

Research was partially supported by a studentship from the Leverhulme Trust.

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Bennett, P. Normal forms for semigroup amalgams. Isr. J. Math. 219, 379–410 (2017). https://doi.org/10.1007/s11856-017-1484-0

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  • DOI: https://doi.org/10.1007/s11856-017-1484-0

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