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Uspekhi Mat. Nauk, 1969, Volume 24, Issue 1(145), Pages 47–59 (Mi umn5451)  

This article is cited in 7 scientific papers (total in 7 papers)


Series of articles on the multioperator rings and algebras
Multioperator algebras and clones of polylinear operators

V. A. Artamonov


Abstract: In this paper we consider principal derived polylinear operators on an $\Omega$-algebra $A$ over an infinite field $P$. We clarify them in terms of partial algebras, that is, of clones. The classification allows us also to classify the multioperator structures on a vector space $A$ for various systems of multioperators.
The idea of discussing clones comes from Cohn's book [1] and the papers of Whitlock [2], Khion [3] and Dicker [4]. We also use certain concepts of Higgins [5] relating to partial algebras.
The author expresses his sincere thanks to A. G. Kurosh for his guidance on this work.

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English version:
Russian Mathematical Surveys, 1969, 24:1, 45–57

Bibliographic databases:

UDC: 519.4+519.9
MSC: 47H60, 47C05, 47S10
Received: 30.09.1968

Citation: V. A. Artamonov, “Multioperator algebras and clones of polylinear operators”, Uspekhi Mat. Nauk, 24:1(145) (1969), 47–59; Russian Math. Surveys, 24:1 (1969), 45–57

Citation in format AMSBIB
\Bibitem{Art69}
\by V.~A.~Artamonov
\paper Multioperator algebras and clones of polylinear operators
\jour Uspekhi Mat. Nauk
\yr 1969
\vol 24
\issue 1(145)
\pages 47--59
\mathnet{http://mi.mathnet.ru/umn5451}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=237408}
\zmath{https://zbmath.org/?q=an:0188.04901|0197.29104}
\transl
\jour Russian Math. Surveys
\yr 1969
\vol 24
\issue 1
\pages 45--57
\crossref{https://doi.org/10.1070/RM1969v024n01ABEH001339}


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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. A. G. Kurosh, “Multioperator rings and algebras”, Russian Math. Surveys, 24:1 (1969), 1–13  mathnet  crossref  mathscinet  zmath
    2. S. N. Tronin, O. A. Kopp, “Matrix linear operads”, Russian Math. (Iz. VUZ), 44:6 (2000), 50–59  mathnet  mathscinet  zmath  elib
    3. S. N. Tronin, “Operads in the category of convexors. I”, Russian Math. (Iz. VUZ), 46:3 (2002), 38–46  mathnet  mathscinet  zmath  elib
    4. S. N. Tronin, “Operads in the category of convexors. II”, Russian Math. (Iz. VUZ), 46:5 (2002), 59–67  mathnet  mathscinet  zmath  elib
    5. S. N. Tronin, “Operads and varieties of algebras defined by polylinear identities”, Siberian Math. J., 47:3 (2006), 555–573  mathnet  crossref  mathscinet  zmath  isi  elib
    6. S. N. Tronin, “Superalgebras and operads. I”, Siberian Math. J., 50:3 (2009), 503–514  mathnet  crossref  mathscinet  isi  elib  elib
    7. S. N. Tronin, “On algebras over multicategories”, Russian Math. (Iz. VUZ), 60:2 (2016), 52–61  mathnet  crossref  isi
  • Успехи математических наук Russian Mathematical Surveys
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