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Integral element

In commutative algebra, an element b of a commutative ring B is said to be integral over a subring A of B if b is a root of some monic polynomial over A.

Examples, Integral extensions & Finiteness of integral closure

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Examples

Equivalent definitions

Elementary properties

Integral extensions

Integral closure

Conductor

Finiteness of integral closure

The Grauert–Remmert–de Jong Criterion

Noether's normalization lemma

Integral morphisms

Absolute integral closure

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Integral element

Nodes130
Edges129
Triples0
Avg. degree1.98
Density0.015385
Components1

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Important terminology

displaystyle integral ring closure field extension algebraic ideal integers noetherian subring closed finite domain algebra normal finitely mathfrak operatorname number

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