TITLE

# Properties of finite unrefinable chains of ring topologies

AUTHOR(S)
Arnautov, V.
PUB. DATE
August 2012
SOURCE
Journal of Mathematical Sciences;Aug2012, Vol. 185 Issue 2, p176
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
Let R(+ , Â·) be a nilpotent ring and $\left( {\mathfrak{M}, < } \right)$ be the lattice of all ring topologies on R(+ , Â·) or the lattice of all such ring topologies on R(+ , Â·) in each of which the ring R possesses a basis of neighborhoods of zero consisting of subgroups. Let Ï„ and Ï„â€² be ring topologies from $\mathfrak{M}$ such that $\tau = {\tau_0}{ \prec_\mathfrak{M}}{\tau_1}{ \prec_\mathfrak{M}} \cdots { \prec_\mathfrak{M}}{\tau_n} = \tau ^{\prime}$ . Then k â‰¤ n for every chain $\tau = {\tau ^{\prime}_0} < {\tau ^{\prime}_1} < \cdots < {\tau ^{\prime}_k} = \tau ^{\prime}$ of topologies from $\mathfrak{M}$, and also n = k if and only if ${\tau ^{\prime}_i}{ \prec_\mathfrak{M}}{\tau ^{\prime}_{i + 1}}$ for all 0 â‰¤ i < k.
ACCESSION #
79824183

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