Design Resolution

As a matter of definition, do all factorial designs have resolutions? Sometimes, designs have factors in a +/- table in which none of the factors is a combination of other factors. In such cases where there are no defining relations or generators, there is likely no resolution (which is the length of the smallest word in a defining relation). Would this be an appropriate assumption to make while applying designs to practical scenarios?

Also how is resolution found for irregular/non-orthogonal fractions?