Small congruence distributive varieties: retracts, injectives, equational compactness and amalgamation
The authors consider the relationship between absolute retracts, injectives and equationally compact algebras in finitely generated congruence distributive varieties of algebras with 1-element subalgebras. In particular, they prove that the absolute retracts in such a variety are precisely the injectives in the amalgamation class, that every equationally compact reduced power of a finite absolute retract is an absolute retract. It is shown that any elementary amalgamation class is Horn if and only if it is closed under finite direct products. Some applications to lattice varieties are given.
scientific article; zbMATH DE number 1099695
scientific article