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

S. A. Aleschenko ; V. I. Arnautov

Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2008), pp. 3-8.

Résumé

Let $\phi :(R,\xi )\to (\hat{R},\hat{\xi })$ be an isomorphism of pseudonormed rings. The inequalities ${\displaystyle \frac{\xi (a\cdot b)}{\xi (b)}}\le \hat{\xi }(\phi (a))\le \xi (a)$ are fulfilled for any $a,b\in R\setminus \{0\}$ iff there exists a pseudonormed ring $(\tilde{R},\tilde{\xi })$ such that $(R,\xi )$ is a left ideal in $(\tilde{R},\tilde{\xi })$ and the isomorphism $\phi$ can be extended up to an isometric homomorphism $\tilde{\phi }:(\tilde{R},\tilde{\xi })\to (\hat{R},\hat{\xi })$.

Bibliographie

[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