The ring of integers is the set of integers ...,,, 0, 1, 2, ..., which form aring. This ring is commonly denoted (doublestruckZ), or sometimes (doublestruck I).

More generally, let be anumber field. Then the ring of integers of, denoted, is the set ofalgebraic integers in, which is aring of dimension over, where is theextension degree of over. is also sometimes called themaximal order of.

The Gaussian integers is the ring of integers of, and theEisenstein integers is the ring of integers of, where is aprimitive cube root of unity.

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Portions of this entry contributed byDavidTerr

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Terr, David andWeisstein, Eric W. "Ring of Integers." FromMathWorld--A Wolfram Resource.https://mathworld.wolfram.com/RingofIntegers.html

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