Left quasifield

Definition
A left quasifield is a set $$Q$$ equipped with:


 * A (infix) binary operation $$+$$, called the addition or additive operation.
 * A unary operation $$-$$, called the additive inverse.
 * A constant $$0$$, called zero.
 * A (infix) binary operation $$*$$, called the multiplication.
 * A constant $$1$$ such that $$1 \ne 0$$.

Such that:


 * $$(Q,+,0,-)$$ is a defining ingredient::group.
 * $$(Q \setminus \{ 0 \},*,1,)$$ is a defining ingredient::Moufang loop with multiplication $$*$$ and identity element $$1$$.
 * $$\! a * (b + c) = (a * b) + (a * c)$$ (i.e., we have the left distributive law).
 * $$\! a * x = (b * x) + c$$ has exactly one solution in $$x$$ for any fixed $$a,b,c \in Q$$ with $$a \ne b$$.