Department of Mathematical Sciences Colloquium Series

An Exploration of Ordered Rings

Tien Chih PhD Candidate, The University of Montana

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.

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

Spring 2013 Colloquia & Events Schedule Mathematical Sciences | The University of Montana