"Green" card holders (Legal Aliens) have a right to live and to work in the country, but obviously they don't have "full rights" for every job. But they have a right to apply for citizenship!"
But to apply for a citizenship you must have lived stateside uninterrupted for 5 years. If you leave the country for more than 6 months the time resets. In my case I flew a 8-month contract in Europe, so I had to start all over again.