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Quasi-projectivity over domains

Published online by Cambridge University Press:  17 April 2009

Dmitri Alexeev
Dmitri Alexeev
Affiliation:
Department of MathematicsTulane UniversityNew Orleans LA 70118United States of America e-mail: alexeev@math.tulane.edu
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Abstract

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Let R be an integral domain with quotient field Q. We investigate quasi- and Q-projective ideals, and properties of domains all ideals of which are quasi-projective. It is shown that the so-called l½-generated ideals are quasi-projective, moreover, projective. A module M is quasi-projective if and only if, for a projective ideal P of R, the tensor product M ⊗RP is quasi-projective. Domains whose all ideals are quasi-projective are characterised as almost maximal Prüfer domains. Q is quasi-projective if and only if every proper submodule of Q is complete in its R-topology.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 60 , Issue 1 , August 1999 , pp. 129 - 135
Copyright
Copyright © Australian Mathematical Society 1999

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