Ursul, M. I. Compact nilrings. (English. Russian original) Zbl 0575.16022 Math. Notes 36, 919-922 (1984); translation from Mat. Zametki 36, No. 6, 839-845 (1984). It is proved that: 1) A compact alternative nilring is a nilring of bounded index. 2) In every compact associative ring the lower nilradical (i.e. the Baer radical) coincides with the upper nilradical (i.e. the Köthe radical). Reviewer: V.Arnautov Cited in 2 ReviewsCited in 3 Documents MSC: 16W80 Topological and ordered rings and modules 16N40 Nil and nilpotent radicals, sets, ideals, associative rings 17D05 Alternative rings 16Nxx Radicals and radical properties of associative rings Keywords:compact alternative nilring; nilring of bounded index; Baer radical; Köthe radical PDFBibTeX XMLCite \textit{M. I. Ursul}, Math. Notes 36, 919--922 (1984; Zbl 0575.16022); translation from Mat. Zametki 36, No. 6, 839--845 (1984) Full Text: DOI References: [1] K. A. Zhevlakov, A. M. Slin’ko, I. P. Shestakov, and A. I. Shlrshov, Rings Close to Associative [in Russian], Nauka, Moscow (1978). [2] N. Jacobson, Structure of Rings, Amer. Math. Soc. (1964). [3] N. Bourbaki, General Topology, Addison-Wesley (1966). [4] I. Kaplansky, ?Topological rings,? Am. J. Math.,69, 153-183 (1947). · Zbl 0034.16604 [5] I. N. Herstein, Topics in Ring Theory, Univ. of Chicago Press, Chicago-London (1969). · Zbl 0232.16001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.