A NOTE ON FLAT MODULES OVER $f$-ALGEBRAS

Article Sidebar

PDF
Published: Dec 1, 1991
DOI: https://doi.org/10.5556/j.tkjm.22.1991.4625
Keywords:
Archimedean f-algebra Bezout ring PF-ring fiat module

Main Article Content

BORIS LAVRIČ
Institute of Mathematics, Physics and Mechanics, Jadrm ska 19, 61000 Ljubljana, Yugoslavi

Abstract




Let $A$ be an Archimedean uniformly complete unital $f$-algebra.It is proved that the following conditions are equivalent: (1) $A$ is a Bezout ring; (2) $A$ is a PF-ring; (3) Every ideal of $A$ is flat; (4) Every submodule of a free $A$-module is flat. This extends a result by C. Neville on algebras of type $C(X)$.




Article Details

How to Cite
LAVRIČ, B. (1991). A NOTE ON FLAT MODULES OVER $f$-ALGEBRAS. Tamkang Journal of Mathematics, 22(4), 371–375. https://doi.org/10.5556/j.tkjm.22.1991.4625
Issue
Vol. 22 No. 4 (1991)
Section
Papers
Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

References

N. Bourbaki, Commutative algebra, Addison-Wesley, Reading, 1972.

S. U. Chase, "Direct products of modules," Trans. Amer. Math. Soc. 97 (1960), 457-473.

S. Eilenberg, N. Steenrod, Foundations c,f algebraic -topology, Princeton Univ. Press, Princeton, New Jersey, 1952.

C. Faith, Algebra: rings, modules and categories I, Springer-Verlag, Berlin, Heidelberg, New York, 1973.

L. Gillman, M. Henriksen, "Rings of continuous functions in which every finitely generated ideal is principal," Trans. Amer. Math. Soc. 82 (1956), 366-391.

C. B. Huijsmans, B. de Pagter, "Ideal theory in f -algebras," Trana. Amer. Math. Soc. 269 (1982), 225-245.

C. W. Neville, "Flat C(X)-modules and F-spaces," Math. Proc. Camb. Phil. Soc. 106 (1989), 237-244.

A. C. Zaanen, Riesz spaces II, North-Holland, Amsterdam, 1983.