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On \(\Sigma\)-nilpotent ideals of topological PI-rings. (English. Russian original) Zbl 1179.16027
J. Math. Sci., New York 149, No. 2, 1113-1118 (2008); translation from Fundam. Prikl. Mat. 12, No. 2, 111-118 (2006).
It is proved a topological analog of a result of the first author which states that the Baer radical of a PI-ring having a faithful module with Krull dimension is nilpotent. Sufficient conditions under which the topological Baer radical of a topological ring is \(\Sigma\)-nilpotent are given.
Accordingly, the authors use the following notions for topological rings which are extended from abstract rings: topological Krull dimension, topological Baer radical, \(\Sigma\)-nilpotent ring.
MSC:
16W80 Topological and ordered rings and modules
16P60 Chain conditions on annihilators and summands: Goldie-type conditions
16N40 Nil and nilpotent radicals, sets, ideals, associative rings
16R10 \(T\)-ideals, identities, varieties of associative rings and algebras
16R20 Semiprime p.i. rings, rings embeddable in matrices over commutative rings
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