Hyperstructures and Idempotent Semistructures

  title={Hyperstructures and Idempotent Semistructures},
  author={Jeffrey Eric Tolliver},
Much of this thesis concerns hypergroups, multirings, and hyperfields. These are analogous to abelian groups, rings, and fields, but have a multivalued addition operation. M. Krasner introduced the notion of a valued hyperfield; The prototypical example is K/(1 + mK) where K is a local field. P. Deligne introduced a category of triples whose objects have the form Trn(K) = (OK/m n K ,mK/m n+1 K , ε) where ε : mK/m n+1 K → OK/m n K is the obvious map. In this thesis I relate the category of… CONTINUE READING