Computational Ideal Theory
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.
KeywordsPolynomial Ring Polynomial Expression Finite Basis Head Term Head Reduction
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