  It is shown that, in the variety of ternary rings, the elements of
amalgamated free products have unique normal forms, and, moreover, this variety
satisfies the strong amalgamation property. Applying these statements,
effective codescent morphisms of ternary rings are characterized. In view of
the fact that the category of ternary rings contains the category of
commutative associative unitary rings as a full subcategory, the class of
effective codescent morphisms in the latter category (which, according to the
well-known Joyal-Tierney's criterion, are precisely monomorphisms
$R\rightarrowtail S$ which are pure as monomorphisms of $R$-modules) is
compared with that of morphisms between commutative associative unitary rings
which are effective codescent in the category of ternary rings. It turns out
that the former class is contained in the latter one, but does not coincide
with it.
