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Co-absolutely co-pure modules

Published online by Cambridge University Press:  20 January 2009

V. A. Hiremath
V. A. Hiremath
Affiliation:
Department of Mathematics, Madurai Kamaraj University, Madurai-625 021, India
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B. Maddox [15] defined absolutely pure modules and derived some interesting properties of these modules. C. Megibben [17] continued the study of these modules and found more interesting properties. We introduce in this paper co-absolutely co-pure modules as dual to absolutely pure modules. We first prove that over a commutative classical ring these modules are precisely the flat modules. As a biproduct we get a projective characterization of flat modules over a commutative co-noetherian ring. Secondly, over a quasi-Frobenius ring R, co-absolutely co-pure right R-modules turn out to be projective modules. Finally we get a characterization of almost Dedekind domains in terms of co-absolutely co-pure modules.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 29 , Issue 3 , October 1986 , pp. 289 - 298
Copyright
Copyright © Edinburgh Mathematical Society 1986

References

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