An Exploration of Ordered Rings

Document Type

Presentation Abstract

Presentation Date

3-11-2013

Abstract

The usual study of linear (affine) programming is done over the real numbers or the integers. However, the notion of a maximum or minimum value is sensible over any ring with a well-defined order. However, in general, ordered rings can be very peculiar objects, and may not exhibit all the properties one associates with the real numbers and its sub-rings.

In this talk, we will present some of the properties of ordered and orderable rings, including some historical examples. We will give examples of ordered rings that are potentially non-Archimedean and even non-commutative. We will then discuss how these may present challenges when attempting to do linear (affine) programming over these rings.

Additional Details

Monday, 11 March 2013
3:10 p.m. in Math 103
4:00 p.m. Refreshments in Math Lounge 109

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