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Derivations and Radicals of Polynomial Ideals over Fields of Arbitrary Characteristic

✍ Scribed by E. Fortuna; P. Gianni; B. Trager

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
306 KB
Volume
33
Category
Article
ISSN
0747-7171

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✦ Synopsis

The purpose of this paper is to give a complete effective solution to the problem of computing radicals of polynomial ideals over general fields of arbitrary characteristic. We prove that Seidenberg's "Condition P" is both a necessary and sufficient property of the coefficient field in order to be able to perform this computation. Since Condition P is an expensive additional requirement on the ground field, we use derivations and ideal quotients to recover as much of the radical as possible. If we have a basis for the vector space of derivations on our ground field, then the problem of computing radicals can be reduced to computing pth roots of elements in finite dimensional algebras.

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