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Calculus in f-algebras

Part of: Ordered structures Topological linear spaces and related structures

Published online by Cambridge University Press:  09 April 2009

F. Beukers  and
C. B. Huijsmans
F. Beukers
Affiliation:
Mathematisch InstituutRijksuniversiteit Leiden Wassenaarseweg 80 2333 AL Leiden, The Netherlands
C. B. Huijsmans
Affiliation:
Mathematisch InstituutRijksuniversiteit Leiden Wassenaarseweg 80 2333 AL Leiden, The Netherlands
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Abstract

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Let A be an Archimedean, uniformly complete, semiprime f-algebra and F(X1,…Xn) ∈ R+ [X1,…Xn] a homogeneous polynomial of degree p (p∈ N). It is shown that (F(u 1…unn))1/p exists in A+ for all u1…un ∈ A+.

MSC classification

Secondary: 06F25: Ordered rings, algebras, modules 46A40: Ordered topological linear spaces, vector lattices
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 37 , Issue 1 , August 1984 , pp. 110 - 116
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Beukers, F., Huijsmans, C. B. and de Pagter, B., ‘Unital embedding and complexification of f-algebras’, Math. Z. 183 (1983), 131–144.CrossRefGoogle Scholar
[2]Huijsmans, C. B. and de Pagter, B., ‘Ideal theory in f-algebras’, Trans. Amer. Math. Soc. 269 (1982), 225–245.Google Scholar
[3]Luxemburg, W. A. J. and Zaanen, A. C., Riesz spaces. I, (North-Holland Publ. Co., Amsterdam London, 1971).Google Scholar