FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2002, VOLUME 8, NUMBER 1, PAGES 273-279
A. V. Khokhlov
Abstract
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We study quasi-unitary topological rings and modules
($m \in Rm\ \forall m \in {}_RM$ )
and multiplicative stabilizers
of their subsets. We give the definition of semicompact rings.
The proved statements imply, in particular, that left quasi-unitariness
of a separable ring $R$ is equvivalent to existence of its left unit,
if $R$ has one of the following properties:
1) $R$ is (semi-)compact, 2) $R$ is left linearly compact,
3) $R$ is countably semicompact (countably left linearly compact)
and has a dense countably generated right ideal,
4) $R$ is precompact and has a left stable neighborhood of zero,
5) $R$ has a dense finitely generated right ideal (e. g.
$R$ satisfies the maximum condition for closed right ideals),
6) the module ${}_RR$ is topologically finitely generated and
${}^{\circ}\!R = 0$ .
All articles are published in Russian.
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Last modified: July 8, 2002