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Sibirskii Matematicheskii Zhurnal, 2001, Volume 42, Number 3, Pages 491–506
(Mi smj1438)
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This article is cited in 3 scientific papers (total in 3 papers)
On maximal chains in the lattice of module topologies
V. I. Arnautov, K. M. Filippov Institute of Mathematics and Computer Science, Academy of Sciences of Moldova
Abstract:
Let $(R,\tau_R)$ be a topological ring and ${}_RM$, a left unitary $R$-module. The set $L(M)$ of all $(R,\tau_R)$-module topologies on ${}_RM$ is a complete modular lattice. A topology $\tau\in L(M)$ is $n$-premaximal if in $L(M)$ there exists an inclusion-maximal chain $\tau_>\tau_1>\dots>\tau_n$ such that $\tau_0$ is the largest element in $L(M)$ and $\tau_n=\tau$. Section 1 contains conditions for existence of 1-premaximal Hausdorff topologies on ${}_RM$. Section 2 contains a description of all $n$-premaximal topologies in the case when $(R,\tau_R)$ is a topological skew field whose topology is determined by a real absolute value.
Received: 13.05.1998
Citation:
V. I. Arnautov, K. M. Filippov, “On maximal chains in the lattice of module topologies”, Sibirsk. Mat. Zh., 42:3 (2001), 491–506; Siberian Math. J., 42:3 (2001), 415–427
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https://www.mathnet.ru/eng/smj1438 https://www.mathnet.ru/eng/smj/v42/i3/p491
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