Abstract of S. Markovski, A. Sokolova
Free Basic Process Algebra

A basic process algebra is an algebra with two binary operations $+$,
$\cdot$ and a set of constants $A$, satisfying the laws (BPA1) - (BPA5)
as given in the text. We present a description of free basic process
algebras by using suitable descriptions of free semigroups and free
semilattices.

The description of free basic process algebra is important since in the
theories of process algebras, many more complex structures are built over
the basic process algebras, and in the applications of process algebras
one usually works with free ones.