I have a simple characterization of the absolute retracts in a
variety of algebras: An algebra A is an absolute retract if and only
if it is (i) equationally compact, and (ii) algebraically closed
(i.e. every finite set of equations satisfiable in some extension of
A is already satisfiable in A). In particular, a finite algebra is an
absolute retract if and only if it it is algebraically closed.

From previous work, I know that in a congruence distributive variety
every finite absolute retract is a product of maximal subdirectly
irreducibles (i.e. those s.i.'s that have no proper essential
extensions), and that in lattice varieties, the converse holds as
well.

Thus in a variety of lattices, the finite algebraically closed
lattices are precisely products of maximal subdirectly irreducibles.
E.g., the finite AC distributive lattices are exactly the finite
Boolean lattices, a result apparently due to Schmid (1979).

What I would like to know is the following: (1) Are the above results
already known (and where can I find them)?, and (2) Are there any
significant papers that study algebraically closed algebras in
general (particularly the congruence distributive case)?