Unrefinable chains when taking the infimum in the lattice of ring topologies for a nilpotent ring
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2017-11-20 13:48
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512.556+512.56 (1)
Algebra (410)
SM ISO690:2012
ARNAUTOV, Vladimir, ERMACOVA, Galina. Unrefinable chains when taking the infimum in the lattice of ring topologies for a nilpotent ring. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2017, nr. 2(84), pp. 71-76. ISSN 1024-7696.
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
Numărul 2(84) / 2017 / ISSN 1024-7696 /ISSNe 2587-4322

Unrefinable chains when taking the infimum in the lattice of ring topologies for a nilpotent ring

CZU: 512.556+512.56
MSC 2010: 22A05, 06B30, 22A30

Pag. 71-76

Arnautov Vladimir1, Ermacova Galina2
 
1 Institute of Mathematics and Computer Science ASM,
2 T.G. Shevchenko State University of Pridnestrovie, Tiraspol
 
 
Disponibil în IBN: 16 noiembrie 2017


Rezumat

A nilpotent ring b R and two ring topologies b _ ′′ and b _∗ on b R are constructed such that b _∗ is a coatom (i.e. between the discrete topology _d and b _∗ there no exists ring topologies) and such that between inf{ b _ ′′, b _d} and inf{ b _ ′′, b _∗} there exists an infinite chain of ring topologies in the lattice of all ring topologies of the ring b R .

Cuvinte-cheie
nilpotent ring, ring topology, unrefinable chains, coatoms, infimum of ring topologies,

lattice of ring topologies

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