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Erschienen in:
1993 | OriginalPaper | Buchkapitel
Computational Ideal Theory
verfasst von : Bhubaneswar Mishra
Erschienen in: Algorithmic Algebra
Verlag: Springer New York
Enthalten in: Professional Book Archive
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In the previous chapter, we saw that an ideal in a Noetherian ring admits a finite Gröbner basis (Theorem 2.3.9). However, in order to develop constructive methods that compute a Gröbner basis of an ideal, we need to endow the underlying ring with certain additional constructive properties. Two such properties we consider in detail, are detachability and syzygy-solvability. A computable Noetherian ring with such properties will be referred to as a strongly computable ring.