  The main theorem (Theorem 4.1) of this paper claims that any ring morphism
from an Azumaya algebra of constant rank over a commutative ring to another one
of the same constant rank and over a reduced commutative ring induces a ring
morphism between the centers of these algebras. The second main theorem
(Theorem 5.3) implies (through its Corollary 5.4) that a ring morphism between
two Azumaya algebras of the same constant rank is an isomorphism if and only if
it induces an isomorphism between their centers. As preliminary to these
theorems we also prove a theorem (Theorem 2.8) describing the Brauer group of a
commutative Artin ring and give an explicit proof of the converse of the
Artin-Procesi theorem on Azumaya algebras (Theorem 2.6).
