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Fundam. Prikl. Mat., 1995, Volume 1, Issue 2, Pages 557–559 (Mi fpm75)  

This article is cited in 3 scientific papers (total in 3 papers)

Short communications

On $PI$-rings having a faithful module with Krull dimension

V. T. Markov

M. V. Lomonosov Moscow State University

Abstract: The main result: if a $PI$-ring $R$ has a faithful left module $M$ with Krull dimension, then its prime radical $N$ is nilpotent. Moreover if the left modules $M$ and $N$ are finitely generated then $R$ has left Krull dimension which is equal to Krull dimension of the module $M$.

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Received: 01.01.1995

Citation: V. T. Markov, “On $PI$-rings having a faithful module with Krull dimension”, Fundam. Prikl. Mat., 1:2 (1995), 557–559

Citation in format AMSBIB
\Bibitem{Mar95}
\by V.~T.~Markov
\paper On $PI$-rings having a faithful module with Krull dimension
\jour Fundam. Prikl. Mat.
\yr 1995
\vol 1
\issue 2
\pages 557--559
\mathnet{http://mi.mathnet.ru/fpm75}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1790987}
\zmath{https://zbmath.org/?q=an:0866.16014}


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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. V. V. Tenzina, “Topological Krull dimension”, J. Math. Sci., 139:4 (2006), 6803–6813  mathnet  crossref  mathscinet  zmath
    2. V. T. Markov, V. V. Tenzina, “On $\Sigma$-nilpotent ideals of topological PI-rings”, J. Math. Sci., 149:2 (2008), 1113–1118  mathnet  crossref  mathscinet  zmath  elib  elib
    3. O. A. Pikhtilkova, S. A. Pikhtilkov, “On special Lie algebras having a faithful module with Krull dimension”, Izv. Math., 81:1 (2017), 91–98  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Фундаментальная и прикладная математика
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