Ring of integers

In mathematics, the ring of integers of an algebraic number field K is the ring of all integral elements contained in K. An integral element is a root of a monic polynomial with rational integer coefficients, x + c_n−1x + … + c₀ . This ring is often denoted by O_K or . Since any rational integer number belongs to K and is its integral element, the ring Z is always a subring of O_K.