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integral closure
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(Definition)
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Let $B$ be a ring with a subring $A$ . The integral closure of $A$ in $B$ is the set $A' \subset B$ consisting of all elements of $B$ which are integral over $A$ .
It is a theorem that the integral closure of $A$ in $B$ is itself a ring. In the special case where $A = \mathbb{Z}$ , the integral closure $A'$ of $\mathbb{Z}$ is often called the ring of integers in $B$ .
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"integral closure" is owned by djao.
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Cross-references: theorem, integral, subring, ring
There are 92 references to this entry.
This is version 4 of integral closure, born on 2002-01-05, modified 2002-06-09.
Object id is 1299, canonical name is IntegralClosure.
Accessed 12168 times total.
Classification:
| AMS MSC: | 13B22 (Commutative rings and algebras :: Ring extensions and related topics :: Integral closure of rings and ideals ; integrally closed rings, related rings ) |
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Pending Errata and Addenda
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