# Left quasifield

From Groupprops

## Definition

A **left quasifield** is a set equipped with:

- A (infix) binary operation , called the
*addition*or*additive operation*. - A unary operation , called the
*additive inverse*. - A constant , called
*zero*. - A (infix) binary operation , called the
*multiplication*. - A constant such that .

Such that:

- is a group.
- is a Moufang loop with multiplication and identity element .
- (i.e., we have the left distributive law).
- has exactly one solution in for any fixed with .