If R is a Noetherian ring and A is an Azumaya algebra over R then an ideal
H
(
A
)
H(A)
in R, called the closed socle of A, is defined and it is shown that
H
(
A
)
H(A)
is independent of the representative A in the Brauer group of R. When R is a domain, the behavior of
H
(
A
)
H(A)
under localization and passage to the quotient field is studied, and
H
(
A
)
H(A)
is calculated when R is the affine ring of a real curve.