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Integrally closed
In
mathematics
, more
specifically
in
abstract algebra
, the
concept
of
integrally
closed
has two
meanings
, one for
groups
and one for
rings
.
A
commutative ring
contained in a
commutative
ring
is said to be integrally
closed in
if is
equal to
the
integral closure
of in.
An
ordered group
G
is called integrally closed
if and only if
for all
elements
a
and
b
of
G
, if
a
n
≤
b
for
all natural
n
then
a
≤ 1.
