Abstract
A. P. Pozhidaev proved that each dialgebra may be embedded into a dialgebra with a barunit. As is known, a dialgebra is a vector space with two binary operations satisfying the axioms of a dimonoid. It is natural in this situation to pose the problem about the possibility of adjoining bar-units to dimonoids in a given class and the problem of embedding dimonoids into dimonoids with bar-units.
In the present article these problems are solved for some classes of dimonoids. In particular, we show that it is impossible to adjoin a set of bar-units to a free dimonoid. Also, we solve the problem of embedding an arbitrary dimonoid into a dimonoid with bar-units.
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Original Russian Text Copyright © 2015 Zhuchok A.V.
Starobelsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 56, No. 5, pp. 1037–1053, September–October, 2015; DOI: 10.17377/smzh.2015.56.505.
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Zhuchok, A.V. Dimonoids and bar-units. Sib Math J 56, 827–840 (2015). https://doi.org/10.1134/S0037446615050055
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DOI: https://doi.org/10.1134/S0037446615050055