  In this paper, we extend properties Going Up and Lying Over from ring theory
to the general setting of congruence--modular equational classes, using the
notion of prime congruence defined through the commutator. We show how these
two properties relate to each other, prove that they are preserved by finite
direct products and quotients and provide algebraic and topological
characterizations for them. We also point out many kinds of varieties in which
these properties always hold.
