Your mother does not have to live with you in order to be sponsored by you for a green card. You have to file Forms I-130, I-864, I-485, and G-325A (one for yourself and one for your mother). All forms and instructions are at uscis.gov/forms. Read the instructions and follow them *very* carefully: the success of your application depends on it. Good luck!
Generally a U.S. citizen age 21 or older may petition for a parent to adjust status in the U.S. through an application in the Immediate Relative visa category, and there is no requirement that the parent and child live together or even in the same state. There are many other details, however, that govern eligibility, including details about the parent's entry into the U.S., date of entry, and more. It would be wise for you and your mother to consult with an immigration attorney who, after learning all of the relevant information, would be able to advise about eligibilities, options and strategies and offer legal representation for the process which often is more complex than it may appear.
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