quasifield

In mathematics, a quasifield is an algebraic structure where and are binary operations on , much like a division ring, but with some weaker conditions. All division rings, and thus all fields, are quasifields. Definition A quasifield is a structure, where and are binary operations on , satisfying these axioms: is a group is a loop, where (left distributivity) has exactly one solution for , Strictly speaking, this is the definition of a left quasifield. A right quasifield is similarly defined, but satisfies right distributivity instead. A quasifield satisfying both distributive laws is called a semifield, in the sense in which the term is used in projective geometry.