Geodesic
On an Algebraic Extension of $A(E)$
Matematičeskie zametki, Tome 72 (2002) no. 5, pp. 649-653 
B. T. Batikyan; S. A. Grigoryan. On an Algebraic Extension of $A(E)$. Matematičeskie zametki, Tome 72 (2002) no. 5, pp. 649-653. http://geodesic.mathdoc.fr/item/MZM_2002_72_5_a1/
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     title = {On an {Algebraic} {Extension} of $A(E)$},
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Voir la notice de l'article provenant de la source Math-Net.Ru

An algebraic extension of the algebra $A(E)$, where $E$ is a compactum in $\mathbb C$ with nonempty connected interior, leads to a Banach algebra $B$ of functions that are holomorphic on some analytic set $K^\circ \subset \mathbb C^2$ with boundary $bK$ and continuous up to $bK$. The singular points of the spectrum of $B$ and their defects are investigated. For the case in which $B$ is a uniform algebra, the depth of $B$ in the algebra $C(bK)$ is estimated. In particular, conditions under which $B$ is maximal on $bK$ are obtained.

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