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The Least Dimonoid Congruences on Free \(\boldsymbol{n}\)-Nilpotent Trioids

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Abstract

Loday and Ronco introduced the notion of a trioid. We construct a trioid which is isomorphic to the free \(n\)-nilpotent trioid, and characterize the least dimonoid congruences and the least semigroup congruence on it. We also study separately singly generated free \(n\)-nilpotent trioids.

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Authors and Affiliations

  1. Department of Algebra and System Analysis, Luhansk Taras Shevchenko National University, 92703, Starobilsk, Ukraine

    A. V. Zhuchok

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  1. A. V. Zhuchok
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Correspondence to A. V. Zhuchok.

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(Submitted by M. M. Arslanov)

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Zhuchok, A.V. The Least Dimonoid Congruences on Free \(\boldsymbol{n}\)-Nilpotent Trioids. Lobachevskii J Math 41, 1747–1753 (2020). https://doi.org/10.1134/S199508022009036X

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  • DOI: https://doi.org/10.1134/S199508022009036X

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