Definition 2.1
(Valuation)
.
Let
K
be a field. A valuation on
K
is a function
v
:
K
×
→
ℝ
such that
(i)
v
(
x
y
)
=
v
(
x
)
+
v
(
y
)
(ii)
v
(
x
+
y
)
≥
min
(
v
(
x
)
,
v
(
y
)
)