Ring of integers

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Ring of integers

DbpediaThing

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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, xn + cn−1xn−1 + … + c0 . This ring is often denoted by OK or . Since any integer number belongs to K and is its integral element, the ring Z is always a subring of OK.The ring Z is the simplest possible ring of integers. Namely, Z = OQ where Q is the field of rational numbers. And indeed, in algebraic number theory the elements of Z are often called the "rational integers" because of this.The ring of integers of a number field is the unique maximal order in the field.

English Wikipedia http://en.wikipedia.org/wiki/Ring_of_integers

Spanish wikipedia http://es.wikipedia.org/wiki/Anillo_de_los_n?meros_enteros