"So terraforming may be much more difficult that supposed. Thats my understanding of the current theories anyway. I am not an expert on this, but its related to my area."
It isn't so much the lack of magnetic field as it is simply the lower gravity. Both have an effect though.
My understanding has been that Martian terraforming would be "temporary" in the sense that the native atmosphere/water might only last a "few" million years. I guess the thinking is that by the time the atmosphere noticeably thinned we'd be able to bring in raw materials from just about anywhere. ;-)
Heck, within even a thousand years I'd expect mankind to have the technology to re-melt the Martian core if we felt like it.
It's no the lack of a magnetic field that makes radiation from space dangerous nor the reason why it would be difficult to terraform Mars. A thick atmosphere protects us on Earth from space born radiation. Protection from a magnetic field depends upon polarity of the radiation. The atmosphere is far more effective. Also, if we wanted to warm up Mars, the desired temperature would dictate, via the Boltzmann distribution of temperature dependent molecular velocities, a situation where there would be a significant number of velocities greater than escape velocity for Mars, which has lower gravity than the Earth. If the Earth had the mass of Mars, we would have no atmosphere because we are much warmer. At least Mars can hold onto a tiny fraction of our atmosphere because it is so cold.
I think there are some feats that are reserved for God. I dont think man will have the ability to do this, not before blowing himself up first, unfortunately. Besides, if the enviro whackos survive, they would never permit something like that. I am sure they would find a Martian slug worm that would be harmed.