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Algebra Discrete Math., 2013, Volume 15, Issue 2, Pages 295–304 (Mi adm427)  

This article is cited in 5 scientific papers (total in 5 papers)

RESEARCH ARTICLE

Free $(\ell r, rr)$-dibands

A. V. Zhuchok

Department of Mathematical Analysis and Algebra, Luhansk Taras Shevchenko National University, Oboronna str., 2, Luhansk, 91011, Ukraine

Abstract: We prove that varieties of $(\ell r, rr)$-dibands and $(\ell n, rn)$-dibands coincide and describe the structure of free $(\ell r, rr)$-dibands. We also show that operations of an idempotent dimonoid with left (right) regular bands coincide, construct a new class of dimonoids and for such dimonoids give an example of a semiretraction.

Keywords: left (right) regular band, $(\ell r, rr)$-diband, diband of subdimonoids, dimonoid, semigroup.

Full text: PDF file (164 kB)
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Bibliographic databases:
MSC: 08B20, 20M10, 20M50, 17A30, 17A32
Received: 03.03.2013
Revised: 03.04.2013
Language:

Citation: A. V. Zhuchok, “Free $(\ell r, rr)$-dibands”, Algebra Discrete Math., 15:2 (2013), 295–304

Citation in format AMSBIB
\Bibitem{Zhu13}
\by A.~V.~Zhuchok
\paper Free $(\ell r, rr)$-dibands
\jour Algebra Discrete Math.
\yr 2013
\vol 15
\issue 2
\pages 295--304
\mathnet{http://mi.mathnet.ru/adm427}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3157323}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Zhuchok, “Cvobodnye $n$-dinilpotentnye dimonoidy”, PFMT, 2013, no. 4(17), 43–46  mathnet
    2. A. V. Zhuchok, “Free $n$-nilpotent dimonoids”, Algebra Discrete Math., 16:2 (2013), 299–310  mathnet  mathscinet
    3. Yurii V. Zhuchok, “Free abelian dimonoids”, Algebra Discrete Math., 20:2 (2015), 330–342  mathnet  mathscinet
    4. A. V. Zhuchok, “Structure of relatively free dimonoids”, Commun. Algebr., 45:4 (2017), 1639–1656  crossref  mathscinet  zmath  isi  scopus
    5. Yu. V. Zhuchok, “Automorphisms of the endomorphism semigroup of a free abelian diband”, Algebra Discret. Math., 25:2 (2018), 322–332  mathnet  mathscinet  zmath  isi
  • Algebra and Discrete Mathematics
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