We wish to construct a minimal set of algebraically independent scalar
curvature invariants formed by the contraction of the Riemann (Ricci) tensor
and its covariant derivatives up to some order of differentiation in three
dimensional (3D) Lorentzian spacetimes. In order to do this we utilize the
Cartan-Karlhede equivalence algorithm since, in general, all Cartan invariants
are related to scalar polynomial curvature invariants. As an example we apply
the algorithm to the class of 3D Szekeres cosmological spacetimes with comoving
dust and cosmological constant $\Lambda$. In this case, we find that there are
at most twelve algebraically independent Cartan invariants, including
$\Lambda$. We present these Cartan invariants, and we relate them to twelve
independent scalar polynomial curvature invariants (two, four and six,
respectively, zeroth, first, and second order scalar polynomial curvature
invariants).
