Interaction term


On a general basis I'm wondering if it is ok (meaningful) to exclude a covariat from a regression model when an interaction is included.


Could we have a model:

Y_i = a1*x_i + a3*(x_i:z_i)

or does the model have to be like this:

Y_i = a1*x_i + a2*z_i + a3*(x_i:z_i) (with a2 close to zero)

if I want to include the interaction term (it is significant).

Thanks for any answers.