Abstract
Inspired by the work of Lorenzen on the theory of ordered groups in the fifties,
we define regular entailment relations and show a crucial theorem for this
structure. We also describe equivariant systems of ideals à la Lorenzen and show
that the remarkable regularisation process invented by him furnishes a regular
entailment relation. By providing constructive objects and arguments, we pursue Lorenzen's aim of ``bringing to light the basic, pure concepts in
their simple and transparent clarity''.