A quasifield (earlier also called a Veblen-Wedderburn system) is an algebraic structure with two binary operations $+$ and $\cdot$ which is weaker than a division ring and which is motivated by synthetic projective geometry. There are the left and right versions. Associative right quasifield is the same as a near-field.

Definition

A left quasifield is an algebraic structure $(A,+,\cdot)$ with two binary operations $+$ and $\cdot$ such that