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Free products of doppelsemigroups

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Abstract

In this paper, we consider doppelsemigroups, which are sets with two binary associative operations satisfying additional axioms. Commutative dimonoids in the sense of Loday are examples of doppelsemigroups and two interassociative semigroups give rise to a doppelsemigroup. The main result of this paper is the construction of the free product of doppelsemigroups. We also construct the free doppelsemigroup, the free commutative doppelsemigroup, the free n-nilpotent doppelsemigroup, and characterize the least commutative congruence and the least n-nilpotent congruence on a free doppelsemigroup.

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

    Anatolii V. Zhuchok

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  1. Anatolii V. Zhuchok
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Correspondence to Anatolii V. Zhuchok.

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Presented by M. Jackson.

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Zhuchok, A.V. Free products of doppelsemigroups. Algebra Univers. 77, 361–374 (2017). https://doi.org/10.1007/s00012-017-0431-6

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  • DOI: https://doi.org/10.1007/s00012-017-0431-6

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