Properties of one-sided ideals of topological rings

V. I. Arnautov

Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2006), pp. 3-14.

Résumé

A continuous ring isomorphism $\nu :(R,\tau )\to (\hat{R},\hat{\tau })$ is said to be semitopological from the left (right) in the class $\mathfrak{R}$ provided $(R,\tau )$ is a left ideal (right ideal, ideal) of a topological ring $(\tilde{R},\tilde{\tau })\in \mathfrak{R}$ and $\nu =\tilde{\nu }{|}_R$ for a topological homomorphism $\tilde{\nu }:(\tilde{R},\tilde{\tau })\to (\hat{R},\hat{\tau })$. The article contains several criteria for a continuous homomorphism to be semi-topological from the left (right).

Bibliographie

[1] Arnautov V. I., “A semitopological isomorphism of topological rings”, Mat. issledovaniya, no. 4:2(12), Stiintsa, Kishinev, 1969, 3–16 (in Russian) | MR

[2] Arnautov V. I., “Semitopological isomorphism of topological groups”, Buletinul Academiei de Sţiinţe a Republicii Moldova, Matematica, 2004, no. 1(44), 15–25 | MR | Zbl

[3] Arnautov V. I., Glavatsky S. T., Mikhalev A. V., Introduction to the theory of topological rings and modules, Marcel Dekker, New York–Basel–Hong Kong, 1996 | MR | Zbl