This chapter discusses algorithms and bounds for polynomial rings. A lemma discussed in the chapter combines with the well-known techniques and results of commutative algebra—local–global principles, Krull's intersection theorem, and the primitive element theorem—to obtain many of the bounds. The chapter describes the nonstandard approach. The results on bounds in their nonstandard formulation express very simple relations between two rings, a polynomial ring K[X] and a certain extension K[X]*. The lemma implies that a number A can be computed from (n,d) such that if f ∞ (f1,…fκ), then f = ∑hifi for certain hi ∞ K[X] of degree at most A.
|Original language||English (US)|
|Number of pages||11|
|Journal||Studies in Logic and the Foundations of Mathematics|
|State||Published - Jan 1 1979|
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