Tropical geometry and hyperfields

The notion of multifield is a straightforward generalization of the notion of field. The difference between these notions is that addition in a multifield may be multivalued. Multifields with multivalued addition can be obtained from usual fields via factorization or degeneration. Multifields provide a natural base for tropical geometry. The degenerations relating objects of the classical algebraic geometry to objects studied by the tropical geometry are induced by degenerations of the ground fields to multifields. Multifields appear naturally in other contexts and are of general interest.