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Sibirsk. Mat. Zh., 2009, Volume 50, Number 6, Pages 1356–1369 (Mi smj2055)  

This article is cited in 14 scientific papers (total in 14 papers)

0-dialgebras with bar-unity and nonassociative Rota–Baxter algebras

A. P. Pozhidaev

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We describe all homogeneous structures of Rota–Baxter algebras on a 0-dialgebra with associative bar-unity and give a corollary on the structure of a Rota–Baxter algebra on an arbitrary associative dialgebra with bar-unity as well as a unital associative conformal algebra. We prove that an arbitrary alternative dialgebra may be embedded into an alternative dialgebra with associative barunity. We suggest the definition of variety of dialgebras in the sense of Eilenberg which is equivalent to that introduced earlier by Kolesnikov.

Keywords: dialgebra, bar-unity, adjoining a bar-unity, Rota–Baxter algebra, enveloping algebra, conformal algebra, alternative dialgebra, variety of dialgebras, unital variety.

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English version:
Siberian Mathematical Journal, 2009, 50:6, 1070–1080

Bibliographic databases:

UDC: 512.57
Received: 28.12.2008
Revised: 07.07.2009

Citation: A. P. Pozhidaev, “0-dialgebras with bar-unity and nonassociative Rota–Baxter algebras”, Sibirsk. Mat. Zh., 50:6 (2009), 1356–1369; Siberian Math. J., 50:6 (2009), 1070–1080

Citation in format AMSBIB
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\by A.~P.~Pozhidaev
\paper 0-dialgebras with bar-unity and nonassociative Rota--Baxter algebras
\jour Sibirsk. Mat. Zh.
\yr 2009
\vol 50
\issue 6
\pages 1356--1369
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\jour Siberian Math. J.
\yr 2009
\vol 50
\issue 6
\pages 1070--1080
\crossref{https://doi.org/10.1007/s11202-009-0118-0}
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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. Anatolii V. Zhuchok, “Semilattices of $r$-archimedean subdimonoids”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2011, no. 3, 108–112  mathnet  mathscinet  zmath
    2. Anatolii V. Zhuchok, “Free rectangular dibands and free dimonoids”, Algebra Discrete Math., 11:2 (2011), 92–111  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. 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
    5. Yuliia V. Zhuchok, “On one class of algebras”, Algebra Discrete Math., 18:2 (2014), 306–320  mathnet  mathscinet
    6. Bremner M.R. Sanchez-Ortega J., “Leibniz Triple Systems”, Commun. Contemp. Math., 16:1 (2014), 1350051  crossref  mathscinet  zmath  isi  elib  scopus
    7. A. V. Zhuchok, Yu. V. Zhuchok, “Free commutative $g$-dimonoids”, Chebyshevskii sb., 16:3 (2015), 276–284  mathnet  elib
    8. A. V. Zhuchok, “Dimonoids and bar-units”, Siberian Math. J., 56:5 (2015), 827–840  mathnet  crossref  crossref  isi  elib  elib
    9. Yurii V. Zhuchok, “Automorphisms of the endomorphism semigroup of a free commutative $g$-dimonoid”, Algebra Discrete Math., 21:2 (2016), 309–324  mathnet  mathscinet
    10. Zhang G. Chen Yu., “a New Composition-Diamond Lemma For Dialgebras”, Algebr. Colloq., 24:2 (2017), 323–350  crossref  mathscinet  zmath  isi  scopus
    11. Zhuchok A.V., “Structure of Relatively Free Dimonoids”, Commun. Algebr., 45:4 (2017), 1639–1656  crossref  mathscinet  zmath  isi  scopus
    12. Benito P. Gubarev V. Pozhidaev A., “Rota-Baxter Operators on Quadratic Algebras”, Mediterr. J. Math., 15:5 (2018), 189  crossref  mathscinet  zmath  isi  scopus
    13. A. P. Pozhidaev, “On the Cayley–Dickson process for dialgebras”, Sib. elektron. matem. izv., 16 (2019), 2110–2123  mathnet  crossref
    14. Chen Yu. Zhang G., “Grobner-Shirshov Bases For Commutative Dialgebras”, Commun. Algebr., 47:4 (2019), 1671–1689  crossref  mathscinet  zmath  isi  scopus
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