## On the ideal structure of algebras of LMC-algebra valued functions.(English)Zbl 0812.46045

Summary: Let $$X$$ be a completely regular topological space and $$A$$ a commutative locally $$m$$-convex algebra. We give a description of all closed and in particular closed maximal ideals of the algebra $$C(X,A)$$ ($$=$$ all continuous $$A$$-valued functions defined on $$X$$). The topology on $$C(X,A)$$ is defined by a certain family of seminorms. The compact-open topology of $$C(X,A)$$ is a special case of this topology.

### MSC:

 46J05 General theory of commutative topological algebras 46J20 Ideals, maximal ideals, boundaries 46E40 Spaces of vector- and operator-valued functions 46H05 General theory of topological algebras
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