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On $\Sigma$-nilpotent ideals of topological PI-rings
V. T. Markov, V. V. Tenzina
M. V. Lomonosov Moscow State University
Abstract:
We show that under certain conditions on the topology of a faithful module $M$ over a topological PI-ring $R$, if $M$ has at most countable dual topological Krull dimension, then the closure of the sum of all $\Sigma$-nilpotent ideals of the ring $R$ is a $\Sigma$-nilpotent ideal too, and in the case of a bounded ring $R$ its topological Baer radical is $\Sigma$-nilpotent.
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English version:
Journal of Mathematical Sciences (New York), 2008, 149:2, 1113–1118
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UDC:
512.556
Citation:
V. T. Markov, V. V. Tenzina, “On $\Sigma$-nilpotent ideals of topological PI-rings”, Fundam. Prikl. Mat., 12:2 (2006), 111–118; J. Math. Sci., 149:2 (2008), 1113–1118
Citation in format AMSBIB
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\pages 111--118
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\jour J. Math. Sci.
\yr 2008
\vol 149
\issue 2
\pages 1113--1118
\crossref{https://doi.org/10.1007/s10958-008-0050-z}
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http://mi.mathnet.ru/eng/fpm938 http://mi.mathnet.ru/eng/fpm/v12/i2/p111
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