Geodesic
On some algebraic characteristics of the algebra of all continuous functions on a~locally connected compactum
Sbornik. Mathematics, Tome 35 (1979) no. 5, pp. 681-696

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In the first part of this paper the algebra $C(X)$ is studied, and in the case of a locally connected compactum $X$ a characteristic of the algebra $C(X)$ is given from the point of view of the plentitude of roots of certain algebraic equations that it contains. In the second part a general method is given for constructing uniform algebras $A$ on suitable compacta $X$ which are different from $C(X)$ but have a number of properties in common with $C(X)$ (normality, algebraic closure, complete closure, etc.). In particular, these methods allow us to give, as a general concept, a new solution to a problem of Gleason concerning peak points. Bibliography: 19 titles. 
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     author = {M. I. Karahanyan},
     title = {On some algebraic characteristics of the algebra of all continuous functions on a~locally connected compactum},
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M. I. Karahanyan. On some algebraic characteristics of the algebra of all continuous functions on a~locally connected compactum. Sbornik. Mathematics, Tome 35 (1979) no. 5, pp. 681-696. http://geodesic.mathdoc.fr/item/SM_1979_35_5_a3/