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Fundam. Prikl. Mat., 2008, Volume 14, Issue 7, Pages 189–207 (Mi fpm1184)  

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

Simple and pseudosimple algebras with operators

V. L. Usoltsev

Volgograd State Pedagogical University

Abstract: In this work, algebras with operators, i.e., algebras with an additional system of unary operations acting as endomorphisms with respect to the basic operations, are considered. We find necessary conditions for the simplicity and pseudosimplicity of an arbitrary universal algebra with a fixed operator and explore how several properties of congruences of this algebra depend on the structure of the unary reduct of a given algebra. For algebras with one ternary operation, defined in the standard way and satisfying Mal'cev's identities, and one operator (i.e., unars with Mal'cev's operation), necessary and sufficient conditions for their simplicity and pseudosimplicity are obtained.

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English version:
Journal of Mathematical Sciences (New York), 2010, 164:2, 281–293

Bibliographic databases:

UDC: 512.572

Citation: V. L. Usoltsev, “Simple and pseudosimple algebras with operators”, Fundam. Prikl. Mat., 14:7 (2008), 189–207; J. Math. Sci., 164:2 (2010), 281–293

Citation in format AMSBIB
\Bibitem{Uso08}
\by V.~L.~Usoltsev
\paper Simple and pseudosimple algebras with operators
\jour Fundam. Prikl. Mat.
\yr 2008
\vol 14
\issue 7
\pages 189--207
\mathnet{http://mi.mathnet.ru/fpm1184}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2533608}
\transl
\jour J. Math. Sci.
\yr 2010
\vol 164
\issue 2
\pages 281--293
\crossref{https://doi.org/10.1007/s10958-009-9730-6}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-71649090619}


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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. N. Lata, “Slabo regulyarnye unary so standartnoi maltsevskoi operatsiei”, Chebyshevskii sb., 14:4 (2013), 146–153  mathnet
    2. V. L. Usoltsev, “O strogo prostykh ternarnykh algebrakh s operatorami”, Chebyshevskii sb., 14:4 (2013), 196–204  mathnet
    3. V. L. Usoltsev, “O gamiltonovykh ternarnykh algebrakh s operatorami”, Chebyshevskii sb., 15:3 (2014), 100–113  mathnet
    4. A. N. Lata, “O koatomakh i dopolneniyakh v reshetkakh kongruentsii unarov s maltsevskoi operatsiei”, Chebyshevskii sb., 16:4 (2015), 212–226  mathnet  elib
    5. V. L. Usoltsev, “O gamiltonovom zamykanii na klasse algebr s odnim operatorom”, Chebyshevskii sb., 16:4 (2015), 284–302  mathnet  elib
    6. V. L. Usoltsev, “Algebry Risa i kongruents-algebry Risa v odnom klasse algebr s operatorom i osnovnoi operatsiei pochti edinoglasiya”, Chebyshevskii sb., 17:4 (2016), 157–166  mathnet  crossref  elib
    7. A. N. Lata, “O kongruents–kogerentnykh algebrakh Risa i algebrakh s operatorom”, Chebyshevskii sb., 18:2 (2017), 154–172  mathnet  crossref  elib
  • Фундаментальная и прикладная математика
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