## Description of all closed maximal regular ideals in subalgebras of the algebra $$C(X;A;\sigma)$$.(English)Zbl 1054.46030

Arizmendi, Hugo (ed.) et al., Topological algebras and their applications. Proceedings of the 4th international conference, Oaxaca, Mexico, July 1–5, 2002. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3556-4/pbk). Contemp. Math. 341, 1-15 (2004).
Let $$X$$ be a completely regular Hausdorff space, $$\sigma$$ a compact cover of $$X$$, closed with respect to finite unions. Let $$A$$ be a locally $$m$$-pseudoconvex Hausdorff algebra, a locally pseudoconvex Waelbroeck Hausdorff algebra or an exponentially galbed Hausdorff algebra with bounded elements. Let $$C(X,A;\sigma)$$ be the algebra of all continuous $$A$$-valued functions on $$X$$, endowed the topology of $$\sigma$$-convergence. The main result in this paper is a description of closed maximal regular one-sided and two-sided ideals in subalgebras of $$C(X,A;\sigma)$$.
For the entire collection see [Zbl 1031.46002].

### MSC:

 46H10 Ideals and subalgebras 46H05 General theory of topological algebras 46H20 Structure, classification of topological algebras