B. T. Batikyan
Point derivations on algebraic extension of Banach algebra
(Lobachevskii Journal of Mathematics, Vol.6, pp.33-37)

It is shown that a point $y_0$ in the carrier space of algebraic extension $B$ of commutative Banach algebra $A$ is a branch point if and only if there exists a local point derivation on $B$ at $y_0$, whose kernel contains $A$.

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