Literature cited
N. Bourbaki, Commutative Algebra, Addison-Wesley, Reading, Massachusetts (1972).
K. Hoffman, Banach Spaces of Analytic Functions, Prentice-Hall, Englewood Cliffs (1962).
W. Rudin, “The closed ideals in an algebra of continuous functions,” Can. J. Math.,9, No. 3, 426–434 (1957).
L. Carleson, “Sets of uniqueness for functions regular in the unit circle,” Acta Math.,87, 325–345 (1952).
B. I. Korenblyum, “On functions which are holomorphic in the disk and smooth up to its boundary,” Dokl. Akad. Nauk SSSR,200, No. 1, 24–27 (1971).
W. T. Novinger, “Holomorphic functions with infinitely differentiable boundary values,” Illinois J. Math.,15, No. 1, 80–90 (1971).
B. I. Korenblyum, “Closed ideals in the ring An,” Functional Anal. Appl.,6, No, 3, 203–214 (1972).
B. A. Taylor and D. L. Williams, “Ideals in rings of analytic functions with smooth boundary values,” Can. J. Math.,22, No. 6, 1266–1283 (1970).
B. Malgrange, Ideals of Differentiable Functions, Oxford Univ. Press, London (1966).
G. M. Goluzin, Geometric Theory of Functions of a Complex Variable, Amer. Math. Soc., Providence (1969).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 65, pp. 149–160, 1976.
Rights and permissions
About this article
Cite this article
Khrushchev, S.V. Every ideal of the ring C nA is principalis principal. J Math Sci 16, 1150–1158 (1981). https://doi.org/10.1007/BF02427723
Issue Date:
DOI: https://doi.org/10.1007/BF02427723