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Mat. Sb. (N.S.), 1971, Volume 85(127), Number 3(7), Pages 307–338 (Mi msb3211)  

This article is cited in 5 scientific papers (total in 6 papers)

On free expansions and algorithmic problems in $R$-varieties of universal algebras

M. M. Glukhov


Abstract: A class of varieties of universal algebras is pointed out (and described by systems of quasi-identities) in which the algorithmic problems of word identity, isomorphism, and occurrence are definitely decidable and in which, as well, theorems on free algebras and free products of algebras hold which are analogous to the theorems of Nielsen–Schreier and Kurosh and certain corollaries of Grushko's grouptheoretic theorem.
Bibliography: 17 titles.

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English version:
Mathematics of the USSR-Sbornik, 1971, 14:3, 297–328

Bibliographic databases:

UDC: 519.4
MSC: Primary 08A05, 08A25, 20E30; Secondary 02B10, 02E10, 10N05
Received: 24.03.1970 and 26.11.1970

Citation: M. M. Glukhov, “On free expansions and algorithmic problems in $R$-varieties of universal algebras”, Mat. Sb. (N.S.), 85(127):3(7) (1971), 307–338; Math. USSR-Sb., 14:3 (1971), 297–328

Citation in format AMSBIB
\Bibitem{Glu71}
\by M.~M.~Glukhov
\paper On free expansions and algorithmic problems in $R$-varieties of universal algebras
\jour Mat. Sb. (N.S.)
\yr 1971
\vol 85(127)
\issue 3(7)
\pages 307--338
\mathnet{http://mi.mathnet.ru/msb3211}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=291053}
\zmath{https://zbmath.org/?q=an:0245.08002}
\transl
\jour Math. USSR-Sb.
\yr 1971
\vol 14
\issue 3
\pages 297--328
\crossref{https://doi.org/10.1070/SM1971v014n03ABEH002619}


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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. T. M. Baranovich, M. S. Burgin, “Linear $\Omega$-algebras”, Russian Math. Surveys, 30:4 (1975), 65–113  mathnet  crossref  mathscinet  zmath
    2. Shabunin L.V., “O konechno opredelennykh totalno simmetricheskikh kvazigruppakh”, Vestn. Chuvashskogo un-ta, 2009, no. 2, 19–24  elib
    3. M. M. Glukhov, “O multiplikativnykh gruppakh svobodnykh i svobodnykh kommutativnykh kvazigrupp”, Chebyshevskii sb., 11:3 (2010), 63–77  mathnet  zmath
    4. V. L. Usoltsev, “Svobodnye algebry mnogoobraziya unarov s maltsevskoi operatsiei $p$, zadannogo tozhdestvom $p(x,y,x)=y$”, Chebyshevskii sb., 12:2 (2011), 127–134  mathnet  mathscinet
    5. M. M. Glukhov, “On the multiplicative groups of free and free commutative quasigroups”, J. Math. Sci., 223:5 (2017), 508–517  mathnet  crossref  mathscinet  elib
    6. “Glukhov Mikhail Mikhailovich (20.11.1930 – 09.12.2018)”, Diskret. matem., 31:1 (2019), 3–6  mathnet  crossref  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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