RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Sibirsk. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Sibirsk. Mat. Zh., 2015, Volume 56, Number 5, Pages 1037–1053 (Mi smj2695)  

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: PDF file (338 kB)
References: PDF file   HTML file

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
\Bibitem{Zhu15}
\by A.~V.~Zhuchok
\paper Dimonoids and bar-units
\jour Sibirsk. Mat. Zh.
\yr 2015
\vol 56
\issue 5
\pages 1037--1053
\mathnet{http://mi.mathnet.ru/smj2695}
\crossref{https://doi.org/10.17377/smzh.2015.56.505}
\elib{http://elibrary.ru/item.asp?id=24817494}
\transl
\jour Siberian Math. J.
\yr 2015
\vol 56
\issue 5
\pages 827--840
\crossref{https://doi.org/10.1134/S0037446615050055}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000363722400005}
\elib{http://elibrary.ru/item.asp?id=25179618}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84944893795}


Linking options:
  • http://mi.mathnet.ru/eng/smj2695
  • http://mi.mathnet.ru/eng/smj/v56/i5/p1037

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Fausto Ongay, Raúl Velásquez, Luis Alberto Wills-Toro, “Normal subdigroups and the isomorphism theorems for digroups”, Algebra Discrete Math., 22:2 (2016), 262–283  mathnet  mathscinet
    2. Anatolii V. Zhuchok, Milan Demko, “Free $n$-dinilpotent doppelsemigroups”, Algebra Discrete Math., 22:2 (2016), 304–316  mathnet  mathscinet
    3. A. V. Zhuchok, A. B. Gorbatkov, “On the structure of dimonoids”, Semigr. Forum, 94:2 (2017), 194–203  crossref  mathscinet  zmath  isi  scopus
    4. A. V. Zhuchok, “Structure of relatively free dimonoids”, Commun. Algebr., 45:4 (2017), 1639–1656  crossref  mathscinet  zmath  isi  scopus
    5. A. V. Zhuchok, K. Knauer, “Abelian doppelsemigroups”, Algebra Discret. Math., 26:2 (2018), 290–304  mathnet  mathscinet  zmath  isi
    6. Yu. M. Movsisyan, “On functional equations and distributive second order formulae with specialized quantifiers”, Algebra Discret. Math., 25:2 (2018), 269–285  mathnet  mathscinet  zmath  isi
  • Сибирский математический журнал Siberian Mathematical Journal
    Number of views:
    This page:162
    Full text:35
    References:31
    First page:4

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019