Abstract
Let ℑ be a Gabriel topology on A, and let q: Mod-A → Mod-Aℑbe the localization functor q(M) = Mℑ. There is a natural transformation Θ: · ⊗ A Aℑ → q (Chap. IX, §1), which in many important cases actually is a natural equivalence (e.g. for rings of fractions). In these cases, q must be an exact functor and thus Aℑ is flat as a left A-module. But there are several other nice properties of rings of fractions which also extend to these cases. One such property, which turns out to be of particular significance, is that every ring homomorphism from Aℑ is completely determined by its restriction to A, i.e. A → Aℑ is an epimorphism in the category of rings.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1975 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Stenström, B. (1975). Perfect Localizations. In: Rings of Quotients. Die Grundlehren der mathematischen Wissenschaften, vol 217. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-66066-5_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-66066-5_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-66068-9
Online ISBN: 978-3-642-66066-5
eBook Packages: Springer Book Archive