Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2008), pp. 3-8
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S. A. Aleschenko; V. I. Arnautov. Properties of one-sided ideals of pseudonormed rings when taking the quotient rings. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2008), pp. 3-8. http://geodesic.mathdoc.fr/item/BASM_2008_3_a0/
@article{BASM_2008_3_a0,
author = {S. A. Aleschenko and V. I. Arnautov},
title = {Properties of one-sided ideals of pseudonormed rings when taking the quotient rings},
journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
pages = {3--8},
year = {2008},
number = {3},
language = {en},
url = {http://geodesic.mathdoc.fr/item/BASM_2008_3_a0/}
}
TY - JOUR
AU - S. A. Aleschenko
AU - V. I. Arnautov
TI - Properties of one-sided ideals of pseudonormed rings when taking the quotient rings
JO - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY - 2008
SP - 3
EP - 8
IS - 3
UR - http://geodesic.mathdoc.fr/item/BASM_2008_3_a0/
LA - en
ID - BASM_2008_3_a0
ER -
%0 Journal Article
%A S. A. Aleschenko
%A V. I. Arnautov
%T Properties of one-sided ideals of pseudonormed rings when taking the quotient rings
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2008
%P 3-8
%N 3
%U http://geodesic.mathdoc.fr/item/BASM_2008_3_a0/
%G en
%F BASM_2008_3_a0
Let $\varphi\colon(R,\xi)\to\bigl(\widehat{R},\widehat{\xi}\bigr)$ 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 $\bigl(\widetilde{R},\widetilde{\xi}\bigr)$ such that $(R,\xi)$ is a left ideal in $\bigl(\widetilde{R},\widetilde{\xi}\bigr)$ and the isomorphism $\varphi$ can be extended up to an isometric homomorphism $\widetilde{\varphi}\colon\bigl(\widetilde{R},\widetilde{\xi}\bigr)\to\bigl(\widehat{R},\widehat{\xi}\bigr)$.
[1] Aleschenko S. A., Arnautov V. I., “Quotient rings of pseudonormed rings”, Buletinul Academiei de Ştiinte a Republicii Moldova, Matematica, 2006, no. 2(51), 3–16 | MR | Zbl
