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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2016, Number 2, Pages 63–70
(Mi basm425)
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This article is cited in 1 scientific paper (total in 1 paper)
Lattice of all topologies of countable module over countable rings
V. I. Arnautova, G. N. Ermakovab
a Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, 5 Academiei str., MD-2028, Chisinau, Moldova
b Transnistrian State University, 25 October str., 128, Tiraspol, 278000, Moldova
Abstract:
For any countable ring $R$ with discrete topology $\tau_0$ and any countable $R$-module $M$ the lattice of all $(R,\tau_0)$-module topologies contains:
– A sublattice which is isomorphic to the lattice of all real numbers with the usual order;
– Two to the power of continuum $(R,\tau_0)$-module topologies each of which is a coatom.
Keywords and phrases:
countable ring, countable module, ring topology, topologies of modules, Hausdorff topology, basis of the filter of neighborhoods, number of topologies of module, the lattice of all topologies of module, coatoms on lattice.
Received: 17.02.2016
Citation:
V. I. Arnautov, G. N. Ermakova, “Lattice of all topologies of countable module over countable rings”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2016, no. 2, 63–70
Linking options:
https://www.mathnet.ru/eng/basm425 https://www.mathnet.ru/eng/basm/y2016/i2/p63
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