[R] main effect & interaction in 2-way ANOVA

[array chip]

Hi,

I am just a little confused of mian effect in the
analysis of variance (ANOVA) when you include or do
not include an interaction term. Let's assume a simple
case of 2-way ANOVA with 2 factors A and B, each with
2 levels. If it shows that main effect for A is
significant when the interaction between A and B is
NOT included, and the main effect for A is NOT
significant when the interaction is included, what
simply does this difference mean? I understand that
main effect for A generally means averaging over
levels of B, is this explanation for the situation
when interaction is included or is not included or is
irrelavant?

And if my interest is in the main effect of A, in the
above senario, should I include the interaction (thus
lose the significance) or not include the interaction
(thus keep my significance)?

Thanks!