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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2017, Number 2, Pages 71–76
(Mi basm451)
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This article is cited in 2 scientific papers (total in 2 papers)
Research articles
Unrefinable chains when taking the infimum in the lattice of ring topologies for a nilpotent ring
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:
A nilpotent ring $\widehat R$ and two ring topologies $\widehat\tau''$ and $ \widehat\tau*$ on $\widehat R$ are constructed such that $\widehat\tau*$ is a coatom (i.e. between the discrete topology $\tau_d$ and $\widehat\tau*$ there no exists ring topologies) and such that between $\inf\{\widehat\tau'',\widehat\tau_d\}$ and $\inf\{\widehat\tau'',\widehat\tau*\}$ there exists an infinite chain of ring topologies in the lattice of all ring topologies of the ring $\widehat R$.
Keywords and phrases:
nilpotent ring, ring topology, lattice of ring topologies, unrefinable chains, coatoms, infimum of ring topologies.
Received: 02.02.2017
Citation:
V. I. Arnautov, G. N. Ermakova, “Unrefinable chains when taking the infimum in the lattice of ring topologies for a nilpotent ring”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2017, no. 2, 71–76
Linking options:
https://www.mathnet.ru/eng/basm451 https://www.mathnet.ru/eng/basm/y2017/i2/p71
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Abstract page: | 217 | Full-text PDF : | 22 | References: | 21 |
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