EDB — 1ZJ

[1ZJ] An ordered ring \(F\) is a ring with a total order relation \(≤\) for which, for every \(x, y, z ∈ F\),

• \(x ≤ y ⇒ x + z ≤ y + z\);

• \(x, y ≥ 0 ⇒ x · y ≥ 0 \) .

Due to [203]↺↻, if \(F\) is a field, in the second hypothesis we may equivalently write \(x, y {\gt} 0 ⇒ x · y {\gt} 0 \) . (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.