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Let $B$ be a ring with a subring $A$ We will assume that $A$ is contained in the center of $B$ (in particular, $A$ is commutative). An element $x \in B$ is integral over $A$ if there exist elements $a_0, \dots, a_{n-1} \in A$ such that $$ x^n +
a_{n-1} x^{n-1} + \cdots + a_1 x + a_0 = 0. $$ The ring $B$ is integral over $A$ if every element of $B$ is integral over $A$
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"integral" is owned by djao.
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Cross-references: commutative, center, contained, subring, ring
There are 102 references to this entry.
This is version 5 of integral, born on 2002-01-05, modified 2005-02-14.
Object id is 1295, canonical name is Integral.
Accessed 11610 times total.
Classification:
| AMS MSC: | 13B21 (Commutative rings and algebras :: Ring extensions and related topics :: Integral dependence) |
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Pending Errata and Addenda
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