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Uspekhi Mat. Nauk, 1975, Volume 30, Issue 4(184), Pages 61–106 (Mi umn4233)  

This article is cited in 11 scientific papers (total in 11 papers)

Linear $\Omega$-algebras

T. M. Baranovich, M. S. Burgin


Abstract: In this paper we give a brief account of the basic results in the theory of linear $\Omega$-algebras. Particular attention is paid to research of recent years, and the connections of the theory of linear $\Omega$-algebras with other parts of algebra are shown. For some special cases of linear $\Omega$-algebras (ternary algebras, $\Gamma$-rings) only a survey of the literature is given.
With the help of linear $\Omega$-algebras new and simplified proofs of some known results in universal algebra are obtained. Various applications of linear $\Omega$-algebras to functional analysis and differential geometry are described.
A large number of open problems have been included, whose solution would apparently be of interest in the development of the theory of linear $\Omega$-algebras.

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English version:
Russian Mathematical Surveys, 1975, 30:4, 65–113

Bibliographic databases:

UDC: 512+519.4
MSC: 17A40, 17B35, 17A50, 16D40, 46A63
Received: 05.03.1974

Citation: T. M. Baranovich, M. S. Burgin, “Linear $\Omega$-algebras”, Uspekhi Mat. Nauk, 30:4(184) (1975), 61–106; Russian Math. Surveys, 30:4 (1975), 65–113

Citation in format AMSBIB
\Bibitem{BarBur75}
\by T.~M.~Baranovich, M.~S.~Burgin
\paper Linear $\Omega$-algebras
\jour Uspekhi Mat. Nauk
\yr 1975
\vol 30
\issue 4(184)
\pages 61--106
\mathnet{http://mi.mathnet.ru/umn4233}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=417027}
\zmath{https://zbmath.org/?q=an:0366.08005}
\transl
\jour Russian Math. Surveys
\yr 1975
\vol 30
\issue 4
\pages 65--113
\crossref{https://doi.org/10.1070/RM1975v030n04ABEH001512}


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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. V. A. Artamonov, “Lattices of varieties of linear algebras”, Russian Math. Surveys, 33:2 (1978), 155–193  mathnet  crossref  mathscinet  zmath
    2. M. S. Burgin, “Free algebras with continuous systems of operations”, Russian Math. Surveys, 35:3 (1980), 179–184  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. Murray Bremner, “Varieties of Anticommutativen-ary Algebras”, Journal of Algebra, 191:1 (1997), 76  crossref
    4. Murray Bremner, “Identities for the Ternary Commutator”, Journal of Algebra, 206:2 (1998), 615  crossref
    5. Richard E Block, Gary Griffing, “Recognizable Formal Series on Trees and Cofree Coalgebraic Systems”, Journal of Algebra, 215:2 (1999), 543  crossref
    6. Murray Bremner, Irvin Hentzel, “Identities for the Associator in Alternative Algebras”, Journal of Symbolic Computation, 33:3 (2002), 255  crossref
    7. Thomas Curtright, Cosmas Zachos, “Classical and quantum Nambu mechanics”, Phys Rev D, 68:8 (2003), 085001  crossref  isi
    8. 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
    9. S. N. Tronin, “Superalgebras and operads. I”, Siberian Math. J., 50:3 (2009), 503–514  mathnet  crossref  mathscinet  isi  elib  elib
    10. J A de Azcárraga, J M Izquierdo, “Topics on n-ary algebras”, J. Phys.: Conf. Ser, 284 (2011), 012019  crossref
    11. V. A. Artamonov, A. V. Klimakov, A. A. Mikhalev, A. V. Mikhalev, “Primitive and almost primitive elements of Schreier varieties”, J. Math. Sci., 237:2 (2019), 157–179  mathnet  crossref  elib
  • Успехи математических наук Russian Mathematical Surveys
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