  Brown has shown that the Stanley-Reisner ring of the broken circuit complex
of a graph has a linear system of parameters which is defined in terms of the
circuits and cocircuits of the graph. Later on Brown and Sagan conjectured a
special set of monomials - a so-called NBC basis - described in terms of the
circuits and cocircuits of the graph to be a monomial basis for the
corresponding quotient of the Stanley-Reisner ring and proved this to be true
for theta and phi graphs. We generalize the aforementioned linear system of
parameters to broken circuit complexes of regular matroids and transfer the
notion of NBC bases to the general setting of regular matroids. We are able to
obtain the analogous results to the ones of Brown and Sagan in this more
general context. We show a deletion-contraction axiom for the existence of NBC
bases. Using this results we identify two infinite classes of matroids which
have NBC bases and which are the matroid theoretic analogue of theta and phi
graphs.
