Properties of finite unrefinable chains of ring topologies
Let R (+ , · ) be a nilpotent ring and be the lattice of all ring topologies on R (+ , · ) or the lattice of all such ring topologies on R (+ , · ) in each of which the ring R possesses a basis of neighborhoods of zero consisting of subgroups. Let τ and τ′ be ring topologies from such that . Then k ...
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| Veröffentlicht in: | Journal of mathematical sciences (New York, N.Y.) N.Y.), 2012-08, Vol.185 (2), p.176-183 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Let
R
(+
, ·
) be a nilpotent ring and
be the lattice of all ring topologies on
R
(+
, ·
) or the lattice of all such ring topologies on
R
(+
, ·
) in each of which the ring
R
possesses a basis of neighborhoods of zero consisting of subgroups. Let
τ
and
τ′
be ring topologies from
such that
.
Then
k ≤ n
for every chain
of topologies from
, and also
n
=
k
if and only if
for all 0
≤ i |
|---|---|
| ISSN: | 1072-3374 1573-8795 |
| DOI: | 10.1007/s10958-012-0906-0 |