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Sibirskii Matematicheskii Zhurnal, 2015, Volume 56, Number 5, Pages 1037–1053
DOI: https://doi.org/10.17377/smzh.2015.56.505 (Mi smj2695) 		 
This article is cited in 17 scientific papers (total in 17 papers)

Dimonoids and bar-units

A. V. Zhuchok

Lugansk Taras Shevchenko National University, Institute of Physics, Mathematics and Information Technologies, Starobilsk, Ukraine
Full-text PDF (338 kB) Citations (17)
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DOI: https://doi.org/10.17377/smzh.2015.56.505
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.
Keywords: dimonoid, bar-unit, adjoining a set of bar-units, free dimonoid, free rectangular dimonoid, free commutative dimonoid, free $n$-(di)nilpotent dimonoid, semigroup, automorphism group.
Received: 25.08.2014
Revised: 25.05.2015
English version:
Siberian Mathematical Journal, 2015, Volume 56, Issue 5, Pages 827–840
DOI: https://doi.org/10.1134/S0037446615050055
Bibliographic databases:
Document Type: Article
UDC: 512.57+512.579
Language: Russian
Citation: A. V. Zhuchok, “Dimonoids and bar-units”, Sibirsk. Mat. Zh., 56:5 (2015), 1037–1053; Siberian Math. J., 56:5 (2015), 827–840
Citation in format AMSBIB
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    • This publication is cited in the following 17 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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