Geodesic
Generalized bases in certain rings of holomorphic functions
Izvestiya. Mathematics , Tome 6 (1972) no. 3, pp. 564-578.

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Conditions are advanced in the paper which, imposed on a ring of holomorphic functions of several variables and a finite collection of functions in that ring, are sufficient for the whole ring to be generated as the closed ideal spanned by the functions in the collection. 
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D. I. Gurevich. Generalized bases in certain rings of holomorphic functions. Izvestiya. Mathematics , Tome 6 (1972) no. 3, pp. 564-578. http://geodesic.mathdoc.fr/item/IM2_1972_6_3_a7/

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