I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2002, VOLUME 8, NUMBER 1, PAGES 273-279
On existence of unit in semicompact rings and topological rings with
A. V. Khokhlov
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We study quasi-unitary topological rings and modules ( ) and multiplicative stabilizers of
We give the definition of semicompact rings.
The proved statements imply, in particular, that left
quasi-unitariness of a separable ring is equvivalent to
existence of its left unit, if has one of the following
properties: 1) is (semi-)compact,
2) is left linearly
compact, 3) is countably
semicompact (countably left linearly compact) and has a dense
countably generated right ideal, 4) is precompact and
has a left stable neighborhood of zero, 5) has a dense finitely
generated right ideal (e.
maximum condition for closed right ideals), 6) the
topologically finitely generated and .
All articles are
published in Russian.
Last modified: July 8, 2002