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ЖУРНАЛЫ // Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica // Архив

Bul. Acad. Ştiinţe Repub. Mold. Mat., 2017, номер 2, страницы 71–76 (Mi basm451)

Эта публикация цитируется в 2 статьях

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

Аннотация: 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 $\widehat R$.

Ключевые слова и фразы: nilpotent ring, ring topology, lattice of ring topologies, unrefinable chains, coatoms, infimum of ring topologies.

MSC: 22A05, 06B30, 22A30

Поступила в редакцию: 02.02.2017

Язык публикации: английский



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