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, $x + c n -1 x + \dots + c 0$ . This ring is often denoted by $O K$ or $\mathcal O_K$ . Since any rational integer number belongs to $K$ and is its integral element, the ring $Z$ is always a subring of $O K$ .

单词	Ring of integers
释义	Ring of integers 英语百科 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, $x + c n -1 x + \dots + c 0$ . This ring is often denoted by $O K$ or $\mathcal O_K$ . Since any rational integer number belongs to $K$ and is its integral element, the ring $Z$ is always a subring of $O K$ .
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