  We examine noncommutative linear sigma models with U(N) global symmetry
groups at the one-loop quantum level, and contrast the results with our
previous study of the noncommutative O(N) linear sigma models where we have
shown that Nambu-Goldstone symmetry realization is inconsistent with continuum
renormalization. Specifically we find no violation of Goldstone's theorem at
one-loop for the U(N) models with the quartic term ordering consistent with
possible noncommutative gauging of the model. The difference is due to terms
involving noncommutative commutator interactions, which vanish in the
commutative limit. We also examine the U(2), and O(4) linear sigma models with
matter in the adjoint representation, and find that the former is consistent
with Goldstone's theorem at one-loop if we include only trace invariants
consistent with possible noncommutative gauging of the model, while the latter
exhibits violations of Goldstone's theorem of the kind seen in the fundamental
of O(N) for N>2.
