i have power of attorney over my mothers affairs,she is in a nursing home with alzhimers,do i have the right to put her home in my name to protect it

You really need to see an Elder Law attorney but no, you should not put the property in your name-a power of attorney can never be used to benefit the person holding the power. Her home normally isn't counted as a resource when determining eligibility for Medicaid (not Medicare) for a period of 6 months, but once it's clear she will have to stay in a nursing home, then it needs to be sold and the money used for her care.    If you sell it now, the proceeds are a resource that will keep her from being eligible for Medicaid until spent on proper and allowable expenses, primarily her care.  Truly, contact an Elder law attorney. For some preliminary info, google "Medicaid regulations-sale of home" and you'll get an idea of how the system works, or call your local social services  department. Good luck.