Gebäude Mathematik, 9. Etage, Raum 911

In this talk we will introduce the notion of the category of accessible posets, as well as provide numerous examples of accessible posets. In particular, we will show how algebras with multivalued addition such as hypergroups, hyperrings or hyperfields can be regarded as accessible posets. Next, by means of localization and order collapse, we will demonstrate a ``canonical`` way of assigning to each hypergroup (hyperring, hyperfield) a group (ring, field, respectively) with a certain ordering relation. As (abstract) Witt rings are important class of examples of hyperfields, these methods provide new ideas to study some classical problems in the algebraic theory of quadratic forms. Some applications, in particular to Witt equivalnce, will be also discussed. This is joint work with Krzysztof Worytkiewicz.

Prof. Dr. Pawel Gladki

Universytet Slaski, Katowice