Geodesic
On $\Sigma$-nilpotent ideals of topological PI-rings
Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 2, pp. 111-118

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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. 
@article{FPM_2006_12_2_a7,
     author = {V. T. Markov and V. V. Tenzina},
     title = {On $\Sigma$-nilpotent ideals of topological {PI-rings}},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {111--118},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2006_12_2_a7/}
}
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V. T. Markov; V. V. Tenzina. On $\Sigma$-nilpotent ideals of topological PI-rings. Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 2, pp. 111-118. http://geodesic.mathdoc.fr/item/FPM_2006_12_2_a7/