38.94.164.18 at 19:16, 20 December 2022

2022-12-20T19:16:57Z

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In [[mathematics]], more specifically in [[abstract algebra]], the concept of '''integrally closed''' has three meanings:

*A commutative ring <math>R</math> contained in a commutative ring <math>S</math> is said to be [[integral element#Equivalent definitions|integrally closed]] in <math>S</math> if <math>R</math> is equal to the integral closure of <math>R</math> in <math>S</math>.
* An integral domain <math>R</math> is said to be [[Integrally closed domain|integrally closed]] if it is equal to its integral closure in its field of fractions.
*An ordered group ''G'' is called [[integrally closed ordered group|integrally closed]] if for all elements ''a'' and ''b'' of ''G'', if ''a''<sup>''n''</sup> ≤ ''b'' for all natural numbers ''n'' then ''a'' ≤ 1.
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Integrally closed - Revision history

38.94.164.18 at 19:16, 20 December 2022