  We discuss dynamical mass generation for fermions and pseudoscalar fields
(axion-like particles (ALP)), in the context of effective theories containing
Yukawa type interactions between the fermions and ALPs. We discuss both
Hermitian and non-Hermitian Yukawa interactions, which are motivated in the
context of some scenarios for radiative (anomalous) Majorana sterile neutrino
masses in some effective field theories. The latter contain shift-symmetry
breaking Yukawa interactions between sterile neutrinos and ALPs. We show that,
for a Hermitian Yukawa interaction, there is no (pseudo)scalar dynamical mass
generation, but there is fermion dynamical mass generation, provided one adds a
bare (pseudo)scalar mass. The situation is opposite for an anti-Hermitian
Yukawa model: there is (pseudo)scalar dynamical mass generation, but no fermion
dynamical mass generation.In the presence of additional attractive four-fermion
interactions, dynamical fermion mass generation can occur in these models,
under appropriate conditions and range of their couplings.
