Is it possible to define a field $F=\left \{ 0, 1, a \right \}$
where the Additive Inverse condition is expressed as :
$x+x=0 \space \space \forall x\in F$ ?
My doubt comes from reading my book on cryptography talking informally about fields, and saying that in a field:
Every element has an additive inverse (for each x, this means there exists an element -x such that x + (-x) = 0).
However in my case there isn't the element $-a$.