Abstract
The relationship between absolute retracts, injectives and equationally compact algebras in finitely generated congruence distributive varieties with 1- element subalgebras is considered and several characterization theorems are proven. Amongst others, we prove that the absolute retracts in such a variety are precisely the injectives in the amalgamation class and that every equationally compact reduced power of a finite absolute retract is an absolute retract. We also show that any elementary amalgamation class is Horn if and only if it is closed under finite direct products.
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