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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2008, Number 3, Pages 3–8
(Mi basm30)
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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 $\varphi\colon(R,\xi)\to\bigl(\widehat{R},\widehat{\xi}\bigr)$ 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 $\widetilde{\varphi}\colon\bigl(\widetilde{R},\widetilde{\xi}\bigr)\to\bigl(\widehat{R},\widehat{\xi}\bigr)$.
Keywords and phrases:
Pseudonormed rings, quotient rings, one-sided ideals of rings, an isometric homomorphism, semi-isometric isomorphism, canonical homomorphism.
Received: 25.06.2008
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
Linking options:
https://www.mathnet.ru/eng/basm30 https://www.mathnet.ru/eng/basm/y2008/i3/p3
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Abstract page: | 218 | Full-text PDF : | 48 | References: | 56 | First page: | 1 |
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