  We consider the preservation of properties of being finitely generated, being
finitely presented and being residually finite under direct products in the
context of different types of algebraic structures. The structures considered
include Mal'cev algebras (including groups, rings and other classical algebras,
as well as loops), idempotent algebras (including lattices), semigroups, and
algebras in congruence modular varieties. We aim to identify as broad classes
as possible in which the 'expected' preservation results (AxB satisfies
property P if and only if A and B satisfy P) hold, and to exhibit ways in which
they may fail outside those classes.
