On non-discrete topologization of some countable skew fields
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ARNAUTOV, Vladimir, ERMAKOVA, G.. On non-discrete topologization of some countable skew fields. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2021, nr. 1-2(95-96), pp. 84-92. ISSN 1024-7696.
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
Numărul 1-2(95-96) / 2021 / ISSN 1024-7696 /ISSNe 2587-4322

On non-discrete topologization of some countable skew fields

CZU: 512.546+519.47
MSC 2010: 22A05.

Pag. 84-92

Arnautov Vladimir1, Ermakova G.2
 
1 Vladimir Andrunachievici Institute of Mathematics and Computer Science,
2 T.G. Shevchenko State University of Pridnestrovie, Tiraspol
 
 
Disponibil în IBN: 3 decembrie 2021


Rezumat

If for any finite subset M of a countable skew field R there exists an infinite subset S  R such that r · m = m · r for any r 2 S and for any m 2 M, then the skew field R admits: – A non-discrete Hausdorff skew field topology 0. – Continuum of non-discrete Hausdorff skew field topologies which are stronger than the topology 0 and such that sup{1, 2} is the discrete topology for any different topologies 1 and 2; – Continuum of non-discrete Hausdorff skew field topologies which are stronger than 0 and such that any two of these topologies are comparable; – Two to the power of continuum Hausdorff skew field topologies stronger than 0, and each of them is a coatom in the lattice of all skew field topologies of the skew fields.

Cuvinte-cheie
Countable skew fields, center of skew field, topological skew fields, Hausdorff topology, basis of the filter of neighborhoods, number of topologies on countable skew fields, lattice of topologies on skew fields, right Ore condition, ring of right quotients, ring of polynomials in the variable x