3
$\begingroup$

What is a good book on topological rings and modules?

I'm interested in topological rings and modules typically endowed with non-linear topologies, e.g.. non-linearly topologized normed rings.

I have some references at my disposal, but I would like to ask for some here, just in case.

Thanks.

Current references:

Seth Warner: Topological Rings.

Bourbaki, Éléments de Mathématique. Topologie Générale.

Mihail Ursul, Topological rings satisfying compactness conditions.

$\endgroup$
3
  • 2
    $\begingroup$ Andre Weil's basic number theory contains adelic rings (and related rings) which are important in number theory $\endgroup$ Oct 21, 2017 at 1:58
  • 1
    $\begingroup$ Are you interested in topological fields as well? $\endgroup$
    – M.G.
    Oct 21, 2017 at 2:02
  • 2
    $\begingroup$ I think that the (tag:reference-request]) tag would be suitable here. But already all 5 spots for tags are used. $\endgroup$ Oct 21, 2017 at 5:46

1 Answer 1

5
$\begingroup$

Here are 3 references that haven't been mentioned yet. I am not sure if the latter two would be of any use to you, but probably are worth a look.

  • Arnautov, Glavatsky, Mikhalev - Introduction to the Theory of Topological Rings and Modules (1995)
  • Prolla - Topics in Functional Analysis over Valued Division Rings (1982)
  • Shell - Topological Fields and Near-Valuations (1990)
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.