Abstract
It is possible to associate a “geometric” object to an arbitrary commutative ring R. This object will be called Spec (R). If R is a finitely generated integral domain over an algebraically closed field, Spec (R) will be very nearly the same as an affine variety associated to R in Chapter I. However in this section we will be completely indifferent to any special properties that R may or may not have — e.g., whether R has nilpotents or other zero-divisors in it or not; whether or not R has a large subfield over which it is finitely generated or even any subfield at all. We insist only that R be commutative and have a unit element 1.
This is a preview of subscription content, log in via an institution to check access.
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
© 1988 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Mumford, D. (1988). Spec (R). In: The Red Book of Varieties and Schemes. Lecture Notes in Mathematics, vol 1358. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21581-4_11
Download citation
DOI: https://doi.org/10.1007/978-3-662-21581-4_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-50497-9
Online ISBN: 978-3-662-21581-4
eBook Packages: Springer Book Archive