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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Finite codimensional subalgebras of Stein algebras and semiglobally Stein algebras

Authors: Hà Huy Khoái and Nguyen Văn Khuê
Journal: Trans. Amer. Math. Soc. 330 (1992), 503-508
MSC: Primary 32E25; Secondary 30H05, 32E10
MathSciNet review: 1025755
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Abstract: The following theorem is proved: For each finite codimensional subalgebra $ A$ of a Stein algebra $ B$ there exists a natural number $ n$ such that $ B$ is algebraically isomorphic to $ A \oplus {{\mathbf{C}}^n}$.

References [Enhancements On Off] (What's this?)

  • [1] Hans Grauert and Reinhold Remmert, Theory of Stein spaces, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 236, Springer-Verlag, Berlin-New York, 1979. Translated from the German by Alan Huckleberry. MR 580152
  • [2] Robert C. Gunning and Hugo Rossi, Analytic functions of several complex variables, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965. MR 0180696
  • [3] Ha Huy Khoai, On the topology of a class of complex manifolds, Proc. 1st Congress Math., Hanoi, 1971.
  • [4] -, Finiteness of complex analytic spaces, Vietnam Math. J. 1 (1973).
  • [5] -, Finite prolongeability of holomorphic functions on analytic sets, Vietnam Math. J. 3 (1973).

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Article copyright: © Copyright 1992 American Mathematical Society