Bulletin of the Australian Mathematical Society
- Bulletin of the Australian Mathematical Society / Volume 71 / Issue 01 / February 2005, pp 113-119
- Copyright © Australian Mathematical Society 2005
- DOI: http://dx.doi.org/10.1017/S0004972700038065 (About DOI), Published online: 17 April 2009
Research Article
Flat submodules of free modules over commutative Bezout rings
K. Sameia1
a1 Department of Mathematics, Bu Ali Sina University, Hamedan, Iran, e-mail: ipm@samei.ir, Institute for studies in Theoretical, Physics and Mathematics(IPM), Tehran, Iran.
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.
(Received September 06 2004)
- [1] Al-Ezeh, H., Natsheh, M. A. and Hussein, ‘Some properties of the ring of continuous functions’, Arch. Math. (Basel) 51 (1988), 60–64. [OpenURL Query Data] [CrossRef] [MathSciNet] [Google 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. [OpenURL Query Data] [CrossRef] [MathSciNet] [Google 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. [OpenURL Query Data] [CrossRef] [Google Scholar]
- [5] Rotman, J., An introduction to homological algebra, Pure and Applied Maths 148 (Academic. Press, New York, London, 1979). [Google Scholar]
