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Flat C(X)-modules and F spaces

Published online by Cambridge University Press:  28 June 2011

Charles W. Neville
Charles W. Neville
Affiliation:
Department of Mathematics, Central Connecticut State University, Connecticut 06050, U.S.A.
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Abstract

We prove that the following conditions are equivalent: X is an F space; every ideal of C(X) is flat; every submodule of a free C(X)-module is flat.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 106 , Issue 2 , September 1989 , pp. 237 - 244
Copyright
Copyright © Cambridge Philosophical Society 1989

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References

[1] Brookshear, J. G.. Projective ideals in rings of continuous functions. Pacific J. Math. 71 (1977), 313–333.CrossRefGoogle Scholar
[2] Brookshear, J. G.. On projective prime ideals in C(X). Proc. Amer. Math. Soc. 69 (1978), 203–204.Google Scholar
[3] DeMarco, G.. Projectivity of pure ideals. Rend. Sem. Mat. Univ. Padova 68 (1983), 289–304.Google Scholar
[4] Gillman, L. and Henriksen, M.. Concerning rings of continuous functions. Trans. Amer. Math. Soc. 77 (1954), 340–362.CrossRefGoogle Scholar
[5] Gillman, L. and Henriksen, M.. Rings of continuous functions in which every finitely generated ideal is principal. Trans. Amer. Math. Soc. 82 (1956), 366–391.Google Scholar
[6] Gillman, L. and Jerison, M.. Rings of Continuous Functions (Van Nostrand, 1960).CrossRefGoogle Scholar
[7] Glaz, S.. Commutative Coherent Rings. Lecture Notes in Math. (Springer-Verlag, to appear).Google Scholar
[8] Neville, C. W.. When is C(X) a coherent ring? Proc. Amer. Math. Soc. (to appear).Google Scholar
[9] Rotman, J.. Notes on Homological Algebra (Van Nostrand, 1970).Google Scholar
[10] Rotman, J.. An Introduction to Homological Algebra (Academic Press, 1979).Google Scholar
[11] Sikorski, R.. Boolean Algebras, 3rd edition (Springer-Verlag, 1969).CrossRefGoogle Scholar