active oldest votes up vote 3 down vote accepted As you noted, axiom $\rm\,A\!\!-\!\!4\,$ holds true. This axiom asserts that every element $\rm\,a\,$ of a field has an additive inverse $\rm\: -a,\:$ called negative $\rm a\:$ or minus $\rm a\:$ (just as reciprocal denotes multiplicative inverses). One easily checks that such