Effective codescent morphisms of ternary rings

Effective codescent morphisms of ternary rings are characterized. To this end, it is shown that, the variety of ternary rings satisfies the strong amalgamation property, and, moreover, in this variety, the elements of amalgamated free products have unique normal forms. 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.