The semiring of sums of squares in a real field
by
Niels Schwartz
Universität Passau, Germany

The sums of squares in a real field continue to be of fundamental importance in real algebra. So far their internal structure has received little attention. A first trivial observation is that they form a semiring. A closer view at this semiring reveals a surprisingly rich structure, e.g., the entire real valuation theory of the field, including relative real holomorphy rings, can be studied on the level of the semiring. There is an l-group that is canonically attached to the semiring. The relationship between this l-group on the one hand and the semiring on the other hand will be explored.

Date received: December 4, 2002