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On alternative and Jordan locally compact rings. (Russian) Zbl 0623.17013
The following results are proved: (a) If R is a locally compact semi- prime alternative or Jordan ring then the connected component \(R_ 0\) of zero is a topological direct summand and in this case \(R_ 0\) is a finite-dimensional semisimple algebra over the field of reals; (b) a connected alternative or Jordan locally compact ring without nonzero idempotents is nilpotent; (c) the quasiregular radical of a locally compact alternative or Jordan ring is closed. All these results are well known for associative rings (Jacobson, Taussky, Kaplansky).
{Reviewer’s remark. Lemma 1 is true in a more general situation: Let R be a ring with associative powers, in which the closure of every one generated subring is compact. Then idempotents can be lifted modulo every closed ideal.}
Reviewer: M.I.Ursul

MSC:
17D05 Alternative rings
17C50 Jordan structures associated with other structures
22A30 Other topological algebraic systems and their representations
16W80 Topological and ordered rings and modules
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