Geodesic
Integral Extensions of Commutative Banach Algebras
Canadian journal of mathematics, Tome 25 (1973) no. 4, pp. 673-686

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper, we continue the study of integral extensions begun in [7]. Whereas in the previous paper, we dealt exclusively with the extension A[x]/(α(x)), α(x) a monic polynomial over A, we now deal with arbitrary integral extensions. Applications of the results presented herein will be made in subsequent papers.To simplify our presentation, we make the following conventions. By an algebra, we will always mean a commutative complex algebra with an identity element, usually denoted by e 
Jr., John A. Lindberg. Integral Extensions of Commutative Banach Algebras. Canadian journal of mathematics, Tome 25 (1973) no. 4, pp. 673-686. doi: 10.4153/CJM-1973-068-2
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[1] 1. Arens, R. and Hoffman, K., Algebraic extensions of normed algebras, Proc. Amer. Math. Soc. 7 (1956), 203–210. Google Scholar

[2] 2. Björk, J., Integral extensions of Banach algebras (unpublished). Google Scholar

[3] 3. Cole, B., One-point parts and the peak point conjecture, Ph. D. thesis, Yale University, 1968. Google Scholar

[4] 4. Gamelin, T., Uniform algebras (Prentice-Hall, Englewood Cliffs, 1969). Google Scholar

[5] 5. Jacobson, N., Lectures in abstract algebra, Vol. III (Van Nostrand, Princeton, 1964). Google Scholar

[6] 6. Kaplansky, I., Ring isomorphisms of Banach algebras, Can. J. Math. 6 (1954), 374–381. Google Scholar

[7] 7. Lindberg, J., Jr., Algebraic extensions of commutative Banach algebras, Pacific J. Math. 14 (1964), 559–584. Google Scholar

[8] 8. Lindberg, J., Jr., Extensions of algebra norms and applications, Studia Math. 40 (1971), 35–39. Google Scholar

[9] 9. Lindberg, J., Jr., Factorization of polynomials over Banach algebras, Trans. Amer. Math. Soc. 112 (1964), 356–368. Google Scholar

[10] 10. Lindberg, J., Jr., Extensions of norms to integral extensions of normed regular algebras (in preparation). Google Scholar

[11] 11. Lindberg, J., Jr., Polynomials over complete l. m — c. algebras and simple integral extensions, Rev. Roumaine Math. Pures Appl. 17 (1972), 47–63. Google Scholar

[12] 12. Pym, J., Inductive and projective limits of normed spaces, Glasgow Math. J. 9 (1968), 103–105. Google Scholar

[13] 13. Rickart, C., General theory of Banach algebras (Van Nostrand, Princeton, 1960). Google Scholar

[14] 14. Zariski, O. and Samuel, P., Commutative algebra, Vol. I (Van Nostrand, Princeton, 1968). Google Scholar

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