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• W2964870960 abstract "Let A be a commutative ring with unit element and A[x] denote the ring of polynomials in x with coefficients from A. Hilbert's theorem is : - If every ideal in A has a finite basis, then every ideal in A[x] also has a finite basis. The proof of this as given by Van der Waerden in his Moderne Algebra Bd. II gives us no information beyond the fact that every ideal in A [x] has a finite basis. If we just reverse the argument in his proof we will be able to give actually a canonical basis for every ideal in A[x] which will be found to be a powerful tool in several applications." @default.
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• W2964870960 date "1939-01-01" @default.
• W2964870960 modified "2023-09-24" @default.
• W2964870960 title "Canonical Basis for Ideals in a Polynomial Domain Over a Commutative Ring with Finite Basis for Ideals" @default.
• W2964870960 doi "https://doi.org/10.18311/jims/1939/17251" @default.
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