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This article is cited in 6 scientific papers (total in 6 papers)
Dimonoids and bar-units
A. V. Zhuchok Lugansk Taras Shevchenko National University, Institute of Physics, Mathematics and Information Technologies, Starobilsk, Ukraine
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.
DOI:
https://doi.org/10.17377/smzh.2015.56.505
Full text:
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English version:
Siberian Mathematical Journal, 2015, 56:5, 827–840
Bibliographic databases:
UDC:
512.57+512.579 Received: 25.08.2014 Revised: 25.05.2015
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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\jour Siberian Math. J.
\yr 2015
\vol 56
\issue 5
\pages 827--840
\crossref{https://doi.org/10.1134/S0037446615050055}
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Linking options:
http://mi.mathnet.ru/eng/smj2695 http://mi.mathnet.ru/eng/smj/v56/i5/p1037
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A. V. Zhuchok, A. B. Gorbatkov, “On the structure of dimonoids”, Semigr. Forum, 94:2 (2017), 194–203
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A. V. Zhuchok, “Structure of relatively free dimonoids”, Commun. Algebr., 45:4 (2017), 1639–1656
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