  The notion of a pre-truss, that is, a set that is both a heap and a semigroup
is introduced. Pre-trusses themselves as well as pre-trusses in which one-sided
or two-sided distributive laws hold are studied. These are termed near-trusses
and skew trusses respectively. Congruences in pre-trusses are shown to
correspond to paragons defined here as sub-heaps satisfying particular closure
property. Near-trusses corresponding to skew braces and near-rings are
identified through their paragon and ideal structures. Regular elements in a
pre-truss are defined leading to the notion of a (pre-truss) domain. The latter
are described as quotients by completely prime paragons, also defined hereby.
Regular pre-trusses as domains that satisfy the Ore condition are introduced
and the pre-trusses of fractions are defined. In particular, it is shown that
near-trusses of fractions without an absorber correspond to skew braces.
