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Every decidable pseudovariety of abelian groups is completely tame

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It has been shown that the proper, non-locally finite pseudovarieties of abelian groups are not tame with respect to the canonical signature. In this paper, we show that every decidable, proper, non-locally finite pseudovariety of abelian groups is completely tame with respect to a further enlarged implicit signature. This theorem yields as a corollary that a pseudovariety of abelian groups is decidable if and only if it is completely tame.

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Acknowledgements

This work has been done as part of the author’s preparation of a doctoral thesis under the supervision of Prof. Jorge Almeida, whose advice is gratefully acknowledged. This work was partially supported by FCT Doctoral Grant with reference (SFRH/BD/98202/2013). This work also was partially supported by CMUP (UID/MAT/00144/2013), which is funded by FCT (Portugal) with national (MEC) and European structural funds (FEDER), under the partnership agreement PT2020.

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  1. Centro de Matemática e Departamento de Matemática, Faculdade de Ciências, Universidade do Porto, Porto, Portugal

    Khadijeh Alibabaei

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  1. Khadijeh Alibabaei
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Correspondence to Khadijeh Alibabaei.

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Communicated by Benjamin Sternberg.

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Alibabaei, K. Every decidable pseudovariety of abelian groups is completely tame. Semigroup Forum 99, 106–125 (2019). https://doi.org/10.1007/s00233-019-10024-1

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