Semifield

Summary

A semifield is an algebraic structure that satisfies all the axioms of a division ring except possibly the associativity of multiplication. Semifields arise in finite geometry, where each semifield coordinatizes a projective plane, called a semifield plane. Finite semifields that are not fields give non-Desarguesian planes. In other areas, a semifield is a semiring whose nonzero elements form a group under multiplication. This node is about the first meaning.