Divisibility Structure and Finitely Generated Ideals in the Disc Algebra
نویسنده
چکیده
The main purpose of this paper is the following algebraic generalization of the corona theorem for the disc algebra A (D): I f d is a greatest common divisor of the functions f l . . . . . fn cA (D), then there exist functions gl,.",gnEA (D) with d-~flgl q-... q-fngn. This generalization is false for many algebras of holomorphic functions, e. g. in case of the Banach algebra H ~ Under the assumption that a greatest common divisor d exists, also a description of d is given.
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