Canonical extension of an absolute value to a field of fractions?

Question

Question

Let $R$ be an integral domain. We define an extended semiabsolute value on $R$ to be a function $|\cdot|:R\to[0,\infty]$ satisfying:

1. $|0|=0$;
2. $|-x|=|x|$ for all $x\in R$;
3. (Triangle Inequality) $|x+y|\leq |x|+|y|$ for all $x,y\in R$.

Assume that $R$ is equipped with an extended semiabsolute value and let $F$ be the field of fractions of $R$. I want to extend the extended semiabsolute value on $R$ to an extended semiabsolute value on $F$. What would be the most "canonical" extension? It might be okay to put additional assumptions if needed.

Remark

If I include the multiplicity condition (i.e., $|xy|=|x||y|$ for all $x,y\in R$) in the definition of extended semiabsolute values, then I can probably define $|b/a|=|b|/|a|$, although I have not checked the details. However, I do not want to include multiplicity, since absolute values in which I am interested does not have that condition.