Lifting canonical algorithms from a ring R to the ring R[x]
Journal of Symbolic Computation
The structure of polynomial ideals and Grobner bases
SIAM Journal on Computing
Algorithms for Computing Groebner Bases of Polynomial Ideals over Various Euclidean Rings
EUROSAM '84 Proceedings of the International Symposium on Symbolic and Algebraic Computation
Upper and Lower Bounds for the Degree of Groebner Bases
EUROSAM '84 Proceedings of the International Symposium on Symbolic and Algebraic Computation
A critical-pair/completion algorithm for finitely generated ideals in rings
Proceedings of the Symposium "Rekursive Kombinatorik" on Logic and Machines: Decision Problems and Complexity
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It has been proved in [L] that there is no universal degree bound of Gröbner bases when the coefficient ring is Z, where Gröbner bases are defined as in [T]. In this paper we prove that the same result is true for each of the following constructive bases: (1) Gröbner bases in the sense of [Bu]; (2) Gröbner bases in the sense of [KK]; (3) detaching bases in the sense of [A]; (4) Szekeres basis in the sense of [S]. We also discuss several open problems about degree bounds, which are motivated by our examples as well as by results from commutative algebra.