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Certain congruences on free trioids |
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| Authors: | Anatolii V Zhuchok Yuliia V Zhuchok Yurii V Zhuchok |
| Institution: | 1. Department of Algebra and System Analysis, Luhansk Taras Shevchenko National University, Starobilsk, Ukrainezhuchok.av@gmail.com;3. Department of Algebra and System Analysis, Luhansk Taras Shevchenko National University, Starobilsk, Ukraine |
| Abstract: | Loday and Ronco introduced the notion of a trioid and constructed the free trioid of rank 1. This paper is devoted to the study of congruences on trioids. We characterize the least dimonoid congruences and the least semigroup congruence on the free (commutative, rectangular) trioid. |
| Keywords: | Congruence dimonoid free commutative trioid free rectangular trioid free trioid semigroup trioid |