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Associativity-like conditions on protomodular algebras

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Abstract

An associativity-like condition (different from the straightforward generalization of the usual associativity given by the move of parentheses in the relevant expression) for operations of high arity is introduced. Operations satisfying this condition are called consociative. It is proved that the algebraic theory of a variety of universal algebras contains a group operation if and only if it contains a consociative semi-abelian operation.

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Acknowledgements

This work is supported by Shota Rustaveli National Science Foundation of Georgia (Ref.: FR-18-10849).

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  1. A. Razmadze Mathematical Institute, Tbilisi State University, 6 Tamarashvili St., Tbilisi, 0177, Georgia

    Dali Zangurashvili

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  1. Dali Zangurashvili
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Correspondence to Dali Zangurashvili.

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Zangurashvili, D. Associativity-like conditions on protomodular algebras. Algebra Univers. 81, 1 (2020). https://doi.org/10.1007/s00012-019-0630-4

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  • DOI: https://doi.org/10.1007/s00012-019-0630-4

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