  We show that the noncommutative Wess-Zumino (NCWZ) Lagrangian with
permutation terms in the interaction parts is renormalizable at one-loop level
by only a wave function renormalization. When the non-commutativity vanishes,
the logarithmic divergence of the wave function renormalization of the NCWZ
theory is the same as that of the commutative one. Next the algebras of
noncommutative field theories (NCFT's) are studied. From Neother currents, the
field representation for the generators of NCFT's is extracted. Then based on
this representation, the commutation relations between the generators are
calculated for NCFT's. The symmetry properties of NCFT's inferred from these
commutation relations are discussed and compared with those of the commutative
ones.
