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Bul. Acad. Ştiinţe Repub. Mold. Mat., 2008, Number 3, Pages 3–8 (Mi basm30)  

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

Research articles

Properties of one-sided ideals of pseudonormed rings when taking the quotient rings

S. A. Aleschenko, V. I. Arnautova

a Institute of Mathematics and Computer Science, Academy of Sciences of Moldova

Abstract: Let $\varphi\colon(R,\xi)\to(\widehat{R},\widehat{\xi})$ be an isomorphism of pseudonormed rings. The inequalities $\dfrac{\xi(a\cdot b)}{\xi(b)}\leq\widehat{\xi}(\varphi(a))\leq\xi(a)$ are fulfilled for any $a,b\in R\setminus\{0\}$ iff there exists a pseudonormed ring $(\widetilde{R},\widetilde{\xi})$ such that $(R,\xi)$ is a left ideal in $(\widetilde{R},\widetilde{\xi})$ and the isomorphism $\varphi$ can be extended up to an isometric homomorphism $\widetilde{\varphi}\colon(\widetilde{R},\widetilde{\xi})\to(\widehat{R},\widehat{\xi})$.

Keywords and phrases: Pseudonormed rings, quotient rings, one-sided ideals of rings, an isometric homomorphism, semi-isometric isomorphism, canonical homomorphism.

Full text: PDF file (93 kB)
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MSC: 16W60, 13A18
Received: 25.06.2008
Language: English

Citation: S. A. Aleschenko, V. I. Arnautov, “Properties of one-sided ideals of pseudonormed rings when taking the quotient rings”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2008, no. 3, 3–8

Citation in format AMSBIB
\Bibitem{AleArn08}
\by S.~A.~Aleschenko, V.~I.~Arnautov
\paper Properties of one-sided ideals of pseudonormed rings when taking the quotient rings
\jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat.
\yr 2008
\issue 3
\pages 3--8
\mathnet{http://mi.mathnet.ru/basm30}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2478709}
\zmath{https://zbmath.org/?q=an:1168.16025}


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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. Svetlana Aleschenko, “A semi-isometric isomorphism on a ring of matrices”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2014, no. 2, 74–84  mathnet
    2. S. A. Aleschenko, V. I. Arnautov, “Properties of accessible subrings of pseudonormed rings when taking quotient rings”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2017, no. 2, 42–53  mathnet  mathscinet
  • Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
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