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On ideals in certain rings of analytical functions. (English. Russian original) Zbl 0845.32018
Russ. Math. 37, No. 10, 76-79 (1993); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1993, No. 10, 77-80 (1993).
The author studies sufficient conditions for an arbitrary analytic function in a domain \(D \subset \mathbb{C}^n\) to belong to an ideal generated by a certain set of analytic functions in \(D\). As a consequence of the above study the problem on coincidence of the said ideal with the ring of all analytic functions in \(D\) is solved.

32E99 Holomorphic convexity
32A38 Algebras of holomorphic functions of several complex variables