Abstract
A Prüfer domain has all of its finitely generated ideals projective. Countably but not finitely generated ideals must be of projective dimension 1. A standard argument due to Auslander gives an upper bound for the projective dimension of an ideal I. If I is Nk-generated, then I has projective dimension ≆ = k+1. Here we look at how one might get the reverse inequality.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Auslander, M., On the dimension of modules and algebras. III: Global dimension, Hagoya Hath J.,9, 1955, 67.
Kaplansky, I., Projective modules, Ann. of Hath. ,68, 1958, 372.
Osofsky, B., Projective dimension of “nice” directed unions, J. Pure and Applied Algebra, 13, 1978, 179.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1984 Springer-Verlag Wien
About this paper
Cite this paper
L.Osofsky, B. (1984). Projective Dimensions of Ideals of Prufer Domains. In: Göbel, R., Metelli, C., Orsatti, A., Salce, L. (eds) Abelian Groups and Modules. International Centre for Mechanical Sciences, vol 287. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2814-5_26
Download citation
DOI: https://doi.org/10.1007/978-3-7091-2814-5_26
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-81847-3
Online ISBN: 978-3-7091-2814-5
eBook Packages: Springer Book Archive