Homorooty in Rings

The topic of ”Homorooty” (for integer numbers) has been introduced and studied in [2]. There are some applications of the homorooty in studying and solving some Diophantine equations and systems, as an interesting and useful elementary method. As a continuation of the Homorooty, we consider it for arbitrary rings and will study its properties in different rings, especially UFD and homorooty rings (which will be introduced). At last we shall state some applications of homorooty in studying some equations over homorooty rings.