Integral closure of an ideal

id: integral-closure-of-an-ideal-242-1434129
title: Integral closure of an ideal
text: In algebra, the integral closure of an ideal I of a commutative ring R, denoted by I ¯ , is the set of all elements r in R that are integral over I: there exist a i ∈ I i such that It is similar to the integral closure of a subring. For example, if R is a domain, an element r in R belongs to I ¯ if and only if there is a finitely generated R-module M, annihilated only by zero, such that r M ⊂ I M . It follows that I ¯ is an ideal of R I is said to be integrally closed if I = I ¯ . The integral c
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original url: https://en.wikipedia.org/wiki/Integral_closure_of_an_ideal
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date modified: 2023-03-11T14:34:56Z
main entity: {"identifier":"Q17098125","url":"https://www.wikidata.org/entity/Q17098125"}
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fields total: 13
integrity: 13

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