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Commutative Algebra/Integral dependence
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integral dependence Let be a commutative ring, and let be a subring, so that is a ring extension. An element is called integral over if there exists a monic polynomial with coefficients in ,
,
such that .
criteria for
polynomials of integral elements are again integral Let be a ring extension, integral over , . Then is integral over .
Let be a ring extension of such that decomposes into linear factors in ; such an extension always exists.