This article is cited in 2 papers

Research articles

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

S. A. Aleschenko, V. I. Arnautov<sup>a

a</sup> 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.

MSC: 16W60, 13A18

Received: 25.06.2008

Language: English

Bibliographic databases:

• 
•