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Sibirsk. Mat. Zh., 2014, Volume 55, Number 6, Pages 1250–1278 (Mi smj2602)  

This article is cited in 2 scientific papers (total in 2 papers)

On embedding some $G$-filtered rings into skew fields

A. I. Valitskas

Tobolsk State Social Pedagogical Academy, Tobolsk, Russia

Abstract: We consider the filtered rings with filtration $v$ taking values in an ordered group $G$ (or $G$-filtered rings). We prove that if a ring $R$ of this type satisfies the condition
$$ \forall a,b\in R^*\quad\forall\varepsilon\in G\quad\exists x,y\in R^*\qquad v(a\cdot x-b\cdot y)>\varepsilon\cdot v(a\cdot x) $$
then $R$ embeds into a skew field. This skew field $D$ becomes a topological ring in the topology induced by an extension of $v$, while $R\cdot R^{-1}$ is everywhere dense in $D$.

Keywords: ring, group, ordered group, skew field, filtration, prime matrix ideal, Lie algebra, universal enveloping algebra.

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English version:
Siberian Mathematical Journal, 2014, 55:6, 1017–1041

Bibliographic databases:

UDC: 512.552.52+512.552.7
Received: 22.01.2014

Citation: A. I. Valitskas, “On embedding some $G$-filtered rings into skew fields”, Sibirsk. Mat. Zh., 55:6 (2014), 1250–1278; Siberian Math. J., 55:6 (2014), 1017–1041

Citation in format AMSBIB
\Bibitem{Val14}
\by A.~I.~Valitskas
\paper On embedding some $G$-filtered rings into skew fields
\jour Sibirsk. Mat. Zh.
\yr 2014
\vol 55
\issue 6
\pages 1250--1278
\mathnet{http://mi.mathnet.ru/smj2602}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3330033}
\transl
\jour Siberian Math. J.
\yr 2014
\vol 55
\issue 6
\pages 1017--1041
\crossref{https://doi.org/10.1134/S0037446614060056}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000346495200005}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84919439877}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. I. Budkin, “On $2$-closedness of the rational numbers in quasivarieties of nilpotent groups”, Siberian Math. J., 58:6 (2017), 971–982  mathnet  crossref  crossref  isi  elib
    2. A. I. Budkin, “On dominions of the rationals in nilpotent groups”, Siberian Math. J., 59:4 (2018), 598–609  mathnet  crossref  crossref  isi  elib
  • Сибирский математический журнал Siberian Mathematical Journal
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