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Formal Power Series Over Commutative N-Algebras

Published online by Cambridge University Press:  20 November 2018

Ernst August Behrens*
Affiliation:
McMaster University, Hamilton, Ontario
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A Banach algebra P over C with identity element is called an N-algebra if any closed ideal in P is the intersection of maximal ideals. An example is given by the algebra of the continuous C-valued functions on a compact Hausdorff space X under the supremum norm; two others are discussed in § 3.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Behrens, E. A., The arithmetic of the quasi-uniserial semigroups without zero, Can. J. Math. 23 (1971), 507516.Google Scholar
2. Behrens, E. A., Ringtheorie (Bibliographisches Institut, Zurich 1975).Google Scholar
3. Behrens, E. A., Topologically arithmetical rings of continuous functions, Publ. Math. Debrecen 04(1977), 107121.Google Scholar
4. Behrens, E. A., Power series developments in lattice ordered semigroups, Semigroup Forum, to appear.Google Scholar
5. Benedetto, J. J., Spectral synthesis (B. G. Teubner, Stuttgart, 1975).Google Scholar
6. Bourbaki, N., General topology, Part 2 (Hermann, Paris, 1966).Google Scholar
7. Katznelson, Y., Sur les algèbres dont les éléments non-négatifs admettent des racines carrées, Ann. Scient. Ec. Norm. Sup. 77 (1960), 167174.Google Scholar
8. Michael, E. A., Locally multiplicatively-convex topological algebras, Memoirs No. 11 (American Math. Soc, Providence, 1971).Google Scholar
9. Rickart, C. E., General theory of Banach algebras, (1960), Reprint (R. E. Krieger Publ. Co., Huntington, N.Y., 1974).Google Scholar
10. Rudin, W., Real and complex analysis (McGraw-Hill, New York, 1974).Google Scholar
11. Šilov, G., On regular normed rings, Trav. Inst. Math. Stekloff 21, Moscow (1947).Google Scholar
12. Willcox, A. B., Some structure theorems for a class of Banach algebras, Pacific J. Math. 6 (1956), 177192.Google Scholar