Another generalization of Mason’s ABC-theorem
نویسنده
چکیده
The well-known ABC-conjecture is generally formulated as follows: The ABC-conjecture. Consider the set S of triples (A, B, C) ∈ N 3 such that ABC = 0, gcd{A, B, C} = 1 and A + B = C Then for every ǫ > 0, there exists a constant K ǫ such that C ≤ K ǫ · R(ABC) 1+ǫ for all triples (A, B, C) ∈ S, where R(ABC) denotes the square-free part of the product ABC. The ABC-conjecture is studied in many papers, and this article will not be another of them. Instead, we consider an analog of this conjecture for polynomials over C instead of integers: Mason's ABC-theorem: Mason's ABC-theorem. Let f 1 , f 2 , f 3 be polynomials over C without a common factor, not all constant, such that
منابع مشابه
m at h . A G ] 2 8 Ju n 20 07 Constructing ( almost ) rigid rings and a UFD having infinitely generated Derksen and Makar - Limanov invariant
An example is given of a UFD which has infinitely generated Derksen invariant. The ring is “almost rigid” meaning that the Derksen invariant is equal to the Makar-Limanov invariant. Techniques to show that a ring is (almost) rigid are discussed, among which is a generalization of Mason’s abc-theorem. AMS classification: 14R20, 13A50, 13N15.
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