A Euclidean domain is a type of integral domain that allows a form of division with remainder, specifically that for any two elements a and b (where b is not zero), there exist elements q and r such that a = bq + r and either r = 0 or the degree of r is less than the degree of b. This property enables a well-defined algorithm for finding the greatest common divisor (GCD) of two elements, making it an essential structure in the study of rings and number theory.
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