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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

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
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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
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