Stable rank of subalgebras of the ball algebras
HTML articles powered by AMS MathViewer
- by Rudolf Rupp PDF
- Proc. Amer. Math. Soc. 109 (1990), 781-786 Request permission
Abstract:
We show that every subalgebra (in the algebraic sense) of ${A^1}({B_n})$ satisfying the weak Nullstellensatz has stable rank less than or equal to $n$. The results are sharp for $n \leq 2$.References
- H. Bass, $K$-theory and stable algebra, Inst. Hautes Études Sci. Publ. Math. 22 (1964), 5–60. MR 174604
- Gustavo Corach and Fernando Daniel Suárez, Extension problems and stable rank in commutative Banach algebras, Topology Appl. 21 (1985), no. 1, 1–8. MR 808718, DOI 10.1016/0166-8641(85)90052-5
- Gustavo Corach and Fernando Daniel Suárez, Stable rank in holomorphic function algebras, Illinois J. Math. 29 (1985), no. 4, 627–639. MR 806470
- Gustavo Corach and Fernando Daniel Suárez, Dense morphisms in commutative Banach algebras, Trans. Amer. Math. Soc. 304 (1987), no. 2, 537–547. MR 911084, DOI 10.1090/S0002-9947-1987-0911084-4
- J. Dieudonné, Treatise on analysis. Vol. III, Pure and Applied Mathematics, Vol. 10-III, Academic Press, New York-London, 1972. Translated from the French by I. G. MacDonald. MR 0350769
- Walter Rudin, Function theory in the unit ball of $\textbf {C}^{n}$, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 241, Springer-Verlag, New York-Berlin, 1980. MR 601594 R. Rupp, Über den Bass-Stable-Rank komplexer Funktionen-Algebren, Dissertation, Karlsruhe, 1988.
- Rudolf Rupp, Stable rank of holomorphic function algebras, Studia Math. 97 (1990), no. 2, 85–90. MR 1083339, DOI 10.4064/sm-97-2-85-90
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 109 (1990), 781-786
- MSC: Primary 46M20; Secondary 18F25, 19K99, 46J15
- DOI: https://doi.org/10.1090/S0002-9939-1990-1019754-2
- MathSciNet review: 1019754