EDB — 1ZJ

[1ZJ] An ordered ring $F$ is a ring with a total order relation $\le$ for which, for every $x,y,z\in F$,

• $x\le y\Rightarrow x+z\le y+z$;

• $x,y\ge 0\Rightarrow x·y\ge 0$ .

Due to [203]↺↻, if $F$ is a field, in the second hypothesis we may equivalently write $x,y>0\Rightarrow x·y>0$ . (Regarding the second hypothesis, see also [1ZT]↺↻) For further informations see the references in [ 29 ] . We will assume that in an ordered ring the multiplication is commutative.