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Flat submodules of free modules over commutative Bezout rings

Published online by Cambridge University Press:  17 April 2009

K. Samei
K. Samei
Affiliation:
Department of Mathematics, Bu Ali Sina University, Hamedan, Iran, e-mail: [email protected], Institute for studies in Theoretical, Physics and Mathematics(IPM), Tehran, Iran.
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A ring is called Bezout if every finitely generated ideal is principal. We show that every ideal of a commutative Bezout ring R is flat if and only if every submodule of a free R-module is flat. Using this theorem we obtain Neville's theorem.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 71 , Issue 1 , February 2005 , pp. 113 - 119
Copyright
Copyright © Australian Mathematical Society 2005

References

[1]Al-Ezeh, H., Natsheh, M. A. and Hussein, , ‘Some properties of the ring of continuous functions’, Arch. Math. (Basel) 51 (1988), 60–64.CrossRefGoogle Scholar
[2]De Marco, G. and Orsatti, A., ‘Commutative rings in which every prime ideal is contained in a unique maximal ideal’, Proc. Amer. Math. Soc. 30 (1971), 459–466.CrossRefGoogle Scholar
[3]Gillman, L. and Jerison, M., Rings of continuous functions (Springer-Verlag, Berlin, Heidelberg, New York, 1976).Google Scholar
[4]Neville, C.W., ‘Flat C (X)-modules and F spaces’, Math. Proc. Cambridge Philos. Soc. 106 (1989), 237–244.CrossRefGoogle Scholar
[5]Rotman, J., An introduction to homological algebra, Pure and Applied Maths 148 (Academic. Press, New York, London, 1979).Google Scholar