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Algebra Logika, 2011, Volume 50, Number 4, Pages 471–496 (Mi al496)  

This article is cited in 18 scientific papers (total in 18 papers)

Dimonoids

A. V. Zhuchok

National Taras Shevchenko University of Kyiv, The Faculty of Mechanics and Mathematics, Kyiv, Ukraine

Abstract: It is proved that a system of axioms for a dimonoid is independent and Cayley's theorem for semigroups has an analog in the class of dimonoids. A least separative congruence is constructed on an arbitrary dimonoid endowed with a commutative operation. It is shown that an appropriate quotient dimonoid is a commutative separative semigroup. A least separative congruence on a free commutative dimonoid is characterized. It is stated that each dimonoid with a commutative operation is a semilattice of Archimedean subdimonoids, each dimonoid with a commutative periodic semigroup is a semilattice of unipotent subdimonoids, and each dimonoid with a commutative operation is a semilattice of $a$-connected subdimonoids. Different dimonoid constructions are presented.

Keywords: dimonoid, dimonoid with commutative operation, free commutative dimonoid, semilattice of subdimonoids, semigroup.

Full text: PDF file (219 kB)
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English version:
Algebra and Logic, 2011, 50:4, 323–340

Bibliographic databases:

UDC: 512.57+512.579
Received: 20.08.2010
Revised: 25.11.2010

Citation: A. V. Zhuchok, “Dimonoids”, Algebra Logika, 50:4 (2011), 471–496; Algebra and Logic, 50:4 (2011), 323–340

Citation in format AMSBIB
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\paper Dimonoids
\jour Algebra Logika
\yr 2011
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\issue 4
\pages 471--496
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\jour Algebra and Logic
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\vol 50
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\pages 323--340
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    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. 66, no. 2, 2014, 218–231  crossref  mathscinet  zmath  isi  scopus
    2. Anatolii V. Zhuchok, “Free normal dibands”, Algebra Discrete Math., 12:2 (2011), 112–127  mathnet  mathscinet  zmath
    3. A. V. Zhuchok, “Dekompozitsii svobodnykh dimonoidov”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 154, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2012, 93–100  mathnet
    4. Anatolii V. Zhuchok, “Semilattice decompositions of trioids”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2013, no. 1, 130–134  mathnet  mathscinet
    5. A. V. Zhuchok, “Free $(\ell r, rr)$-dibands”, Algebra Discrete Math., 15:2 (2013), 295–304  mathnet  mathscinet
    6. A. V. Zhuchok, “Free $n$-nilpotent dimonoids”, Algebra Discrete Math., 16:2 (2013), 299–310  mathnet  mathscinet
    7. Yuri Movsisyan, Sergey Davidov, Mher Safaryan, “Construction of free $\mathfrak{g}$-dimonoids”, Algebra Discrete Math., 18:1 (2014), 138–148  mathnet  mathscinet
    8. Yurii V. Zhuchok, “The endomorphism semigroup of a free dimonoid of rank 1”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2014, no. 3, 30–37  mathnet
    9. Yuliia V. Zhuchok, “On one class of algebras”, Algebra Discrete Math., 18:2 (2014), 306–320  mathnet  mathscinet
    10. A. V. Zhuchok, Yu. V. Zhuchok, “Free commutative $g$-dimonoids”, Chebyshevskii sb., 16:3 (2015), 276–284  mathnet  elib
    11. A. V. Zhuchok, “Dimonoids and bar-units”, Siberian Math. J., 56:5 (2015), 827–840  mathnet  crossref  crossref  isi  elib  elib
    12. Yuliia V. Zhuchok, “Free rectangular tribands”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2015, no. 2, 61–73  mathnet
    13. A. Zhuchok, Yu. Zhuchok, “Free left $n$-dinilpotent dimonoids”, Semigr. Forum, 93:1 (2016), 161–179  crossref  mathscinet  zmath  isi  scopus
    14. A. V. Zhuchok, A. B. Gorbatkov, “On the structure of dimonoids”, Semigr. Forum, 94:2 (2017), 194–203  crossref  mathscinet  zmath  isi  scopus
    15. A. V. Zhuchok, “Structure of relatively free dimonoids”, Commun. Algebr., 45:4 (2017), 1639–1656  crossref  mathscinet  zmath  isi  scopus
    16. A. V. Zhuchok, “Free products of doppelsemigroups”, Algebr. Universalis, 77:3 (2017), 361–374  crossref  mathscinet  zmath  isi  scopus
    17. A. V. Zhuchok, “Free left $n$-dinilpotent doppelsemigroups”, Commun. Algebr., 45:11 (2017), 4960–4970  crossref  mathscinet  zmath  isi  scopus
    18. A. V. Zhuchok, “Structure of free strong doppelsemigroups”, Commun. Algebr., 46:8 (2018), 3262–3279  crossref  mathscinet  zmath  isi  scopus
  • Алгебра и логика Algebra and Logic
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