Definition 2

Let G be an ordered set. A subset of G is called major if the relations $x \in M$ and $y \geq x$ imply $y \in M$.

Let $K$ be a field, $v$ a valuation on $K$, $A$ the ring of $v$ and $G$ the order group of $v$. For every major subset $M \subset G$, let $a(M)$ be the set of $x \in K$ such that $v(x) \in M \cup \{+\infty\}$. Clearly $a(M)$ is a sub-A-module of $K$.