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Context equivalence of semigroups

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Abstract

Two semigroups are called strongly Morita equivalent if they are contained in a Morita context with unitary bi-acts and surjective mappings. We consider the notion of context equivalence which is obtained from the notion of strong Morita equivalence by dropping the requirement of unitariness. We show that context equivalence is an equivalence relation on the class of factorisable semigroups and describe factorisable semigroups that are context equivalent to monoids or groups, and semigroups with weak local units that are context equivalent to inverse semigroups, orthodox semigroups or semilattices.

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Authors and Affiliations

  1. Institute of Mathematics, University of Tartu, Ülikooli 18, 50090, Tartu, Estonia

    Valdis Laan

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  1. Valdis Laan
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Correspondence to Valdis Laan.

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Communicated by Mária B. Szendrei

This research was supported by the Estonian Science Foundation grant no. 6238, Estonian Targeted Financing Project SF0180039s08, and by the exchange agreement between the Estonian and the Hungarian Academies of Sciences.

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Laan, V. Context equivalence of semigroups. Period Math Hung 60, 81–94 (2010). https://doi.org/10.1007/s10998-010-1081-z

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  • DOI: https://doi.org/10.1007/s10998-010-1081-z

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