Birkhoff's Theorem from a geometric perspective: A simple example

author

  • F. William Lawvere Department of Mathematics, University at Buffalo, Buffalo, New York 14260-2900, United States of America.
Abstract:

‎From Hilbert's theorem of zeroes‎, ‎and from Noether's ideal theory‎, ‎Birkhoff derived certain algebraic concepts (as explained by Tholen) that have a dual significance in general toposes‎, ‎similar to their role in the original examples of algebraic geometry‎. ‎I will describe a simple example that illustrates some of the aspects of this relationship‎. The dualization from algebra to geometry in the basic Grothendieck spirit can be accomplished (without intervention of topological spaces) by the following method‎, ‎known as Isbell conjugacy.

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

birkhoff's theorem from a geometric perspective: a simple example

‎from hilbert's theorem of zeroes‎, ‎and from noether's ideal theory‎, ‎birkhoff derived certain algebraic concepts (as explained by tholen) that have a dual significance in general toposes‎, ‎similar to their role in the original examples of algebraic geometry‎. ‎i will describe a simple example that illustrates some of the aspects of this relationship‎. the dualization from algebra to geometr...

full text

Birkhoff’s Theorem from a geometric perspective: A simple example

From Hilbert’s theorem of zeroes, and from Noether’s ideal theory, Birkhoff [1] derived certain algebraic concepts (as explained by Tholen [10]) that have a dual significance in general toposes, similar to their role in the original examples of algebraic geometry. I will describe a simple example that illustrates some of the aspects of this relationship. The dualization from algebra to geometry...

full text

birkhoff's theorem from a geometric perspective: a simple example

‎from hilbert's theorem of zeroes‎, ‎and from noether's ideal theory‎, ‎birkhoff derived certain algebraic concepts (as explained by tholen) that have a dual significance in general toposes‎, ‎similar to their role in the original examples of algebraic geometry‎. ‎i will describe a simple example that illustrates some of the aspects of this relationship‎. the dualization from algebra ...

full text

The Local Limit Theorem: A Historical Perspective

The local limit theorem describes how the density of a sum of random variables follows the normal curve. However the local limit theorem is often seen as a curiosity of no particular importance when compared with the central limit theorem. Nevertheless the local limit theorem came first and is in fact associated with the foundation of probability theory by Blaise Pascal and Pierre de Fer...

full text

An Integral Geometric Theorem for Simple Valuations

We prove a translative mean value formula for simple valuations, taken at the intersection of a fixed and a translated convex body. MSC 2000: 52A22 (primary); 52B45 (secondary)

full text

Bang-Bang Operations from a Geometric Perspective

Strong, fast pulses, called ‘‘bang–bang’’ controls can be used to eliminate the effects of system-environment interactions. This method for preventing errors in quantum information processors is treated here in a geometric setting which leads to an intuitive perspective. Using this geometric description, we clarify the notion of group symmetrization as an averaging technique, provide a geometri...

full text

My Resources

Save resource for easier access later

Save to my library Already added to my library

{@ msg_add @}


Journal title

volume 4  issue 1

pages  1- 8

publication date 2016-02-01

By following a journal you will be notified via email when a new issue of this journal is published.

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023