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The algebra of almost periodic functions has infinite topological stable rank

Author(s): Fernando Daniel Suárez
Journal: Proc. Amer. Math. Soc. 124 (1996), 873-876.
MSC (1991): Primary 46J10
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Abstract: We show that if $A$ is the uniform algebra of almost periodic functions, then the set $U_n(A)=\{(a_1,\dotsc,a_n)\in A^n\colon \sum _{1\leq j\leq n}Aa_j=A\}$ cannot be dense in $A^n$ for any positive integer $n$ .

References:

1.: T. W. Gamelin, Uniform algebras, Prentice-Hall, Englewood Cliffs, NJ, 1969. MR 53:14137
2.: G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, Clarendon Press, Oxford, 1979. MR 81i:10002
3.: R. H. Herman and L. N. Vaserstein, The stable range of -algebras, Invent. Math. 77 (1984), 553--555. MR 86a:46074
4.: J. Nagata, Modern Dimension Theory, revised and extended version, Heldermann Verlag, Berlin, 1983. MR 84h:54033
5.: M. Rieffel, Dimension and stable rank in the -theory of -algebra, Proc. London Math. Soc. 46 (1983), 301--333. MR 84g:46085

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Additional Information:

Fernando Daniel Suárez
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
Address at time of publication: Instituto Argentino de Matemática, Vio monte 1636-1o Cpo.-1o Piso, 1055 Buenos Aires, Argentina

DOI: 10.1090/S0002-9939-96-03200-5
PII: S 0002-9939(96)03200-5
Keywords: Almost periodic functions, unimodulars, topological stable rank
Received by editor(s): July 12, 1994
Received by editor(s) in revised form: September 22, 1994
Additional Notes: The author is a Fellow of the John Simon Guggenheim Memorial Foundation
Communicated by: Dale Alspach
Copyright of article: Copyright 1996, American Mathematical Society


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