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Fundam. Prikl. Mat., 2012, Volume 17, Issue 5, Pages 55–68 (Mi fpm1433)  

This article is cited in 2 scientific papers (total in 2 papers)

On $l$-prime radicals of lattice ordered algebras

J. V. Kochetova

Moscow State Pedagogical University

Abstract: The Kopytov order for any algebras over a field is considered. The purpose of this paper is to investigate a generalization of the concept of prime radical to lattice ordered algebras over partially ordered fields. Prime radicals of $l$-algebras over partially ordered and directed fields are described. Some results concerning properties of the lower weakly solvable $l$-radical of $l$-algebras are obtained. Necessary and sufficient conditions for the $l$-prime radical of an $l$-algebra to be equal to the lower weakly solvable $l$-radical of an $l$-algebra are presented.

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English version:
Journal of Mathematical Sciences (New York), 2013, 193:4, 516–525

UDC: 512.552+512.545

Citation: J. V. Kochetova, “On $l$-prime radicals of lattice ordered algebras”, Fundam. Prikl. Mat., 17:5 (2012), 55–68; J. Math. Sci., 193:4 (2013), 516–525

Citation in format AMSBIB
\Bibitem{Koc12}
\by J.~V.~Kochetova
\paper On $l$-prime radicals of lattice ordered algebras
\jour Fundam. Prikl. Mat.
\yr 2012
\vol 17
\issue 5
\pages 55--68
\mathnet{http://mi.mathnet.ru/fpm1433}
\transl
\jour J. Math. Sci.
\yr 2013
\vol 193
\issue 4
\pages 516--525
\crossref{https://doi.org/10.1007/s10958-013-1478-3}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84899418054}


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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. Yu. V. Kochetova, “Pervichnyi radikal $\mathcal{K}$-uporyadochennykh algebr kak radikal v smysle Kurosha”, Chebyshevskii sb., 14:3 (2013), 65–74  mathnet
    2. J. V. Kochetova, “Radical properties of lattice $\mathcal{K}$-ordered algebras”, J. Math. Sci., 230:3 (2018), 411–413  mathnet  crossref  mathscinet
  • Фундаментальная и прикладная математика
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