Let
D
D
be an integral domain. A saturated multiplicatively closed subset
S
S
of
D
D
is a splitting set if each nonzero
d
∈
D
d\in D
may be written as
d
=
s
a
d=sa
where
s
∈
S
s\in S
and
s
′
D
∩
a
D
=
s
′
a
D
s’D\cap aD=s’aD
for all
s
′
∈
S
s’\in S
. We show that if
S
S
is a splitting set in
D
D
, then
S
U
(
D
N
)
SU(D_{N})
is a splitting set in
D
N
D_{N}
,
N
N
a multiplicatively closed subset of
D
D
, and that
S
⊆
D
S\subseteq D
is a splitting set in
D
[
X
]
⟺
S
D[X]\iff S
is an lcm splitting set of
D
D
, i.e.,
S
S
is a splitting set of
D
D
with the further property that
s
D
∩
d
D
sD\cap dD
is principal for all
s
∈
S
s\in S
and
d
∈
D
d\in D
. Several new characterizations and applications of splitting sets are given.