Another Elementary Proof of the Nullstellensatz
نویسنده
چکیده
1. P. Flajolet and A. Odlyzko, Singularity analysis of generating functions, SIAM J. Discrete Math. 3 (1990) 216–240. 2. R. E. Greenwood, The number of cycles associated with the elements of a permutation group, this MONTHLY 60 (1953) 407–409. 3. J. Konvalina, A unified interpretation of the binomial coefficients, the Stirling numbers, and the Gaussian coefficients, this MONTHLY 107 (2000) 901–910. 4. L. Milne-Thomson, The Calculus of Finite Differences, Chelsea, New York, 1981.
منابع مشابه
A New Proof of Hilbert's Nullstellensatz
Introduction. A number of proofs of Hubert 's Nullstellensatz can be found in the literature. One, based on elimination theory and due to A. Rabinowitsch, is reproduced in van der Waerden's Moderne Algebra, vol. 2, p. 11. In a later chapter van der Waerden gives another proof which is based on the method of specialization in fields of algebraic functions (pp. 59-61). The finishing touches to th...
متن کاملLower bounds on Nullstellensatz proofs via designs
The Nullstellensatz proof system is a proof system for propositional logic based on algebraic identities in fields. Prior work has proved lower bounds of the degree Nullstellensatz refutations using combinatorial constructions called designs. This paper surveys the use of designs for Nullstellensatz lower bounds. We give a new, more general definition of designs. We present an explicit construc...
متن کاملA Short Proof for the Krull Dimension of a Polynomial Ring
A first important result in dimension theory is the fact that the Krull dimension of the ring K[X1, . . . , X`] is equal to ` when K is a field. In the literature this result is always obtained after some preliminary efforts that seem excessive for settling such an intuitive fact. For example, many authors rely on the principal ideal theorem of Krull, whose proof is very tricky. Matsumura [6,ch...
متن کاملCorona-Type Theorems and Division in Some Function Algebras on Planar Domains
Let A be an algebra of bounded smooth functions on the interior of a compact set in the plane. We study the following problem: if f , f1, . . . , fn ∈ A satisfy | f | ≤ ∑nj=1 | f j|, does there exist g j ∈ A and a constant N ∈ N such that f N = ∑n j=1 g j f j? A prominent role in our proofs is played by a new space, C∂,1(K), which we call the algebra of ∂-smooth functions. In the case n = 1, a ...
متن کاملOn a generalization of Stickelberger's Theorem
We prove two versions of Stickelberger’s Theorem for positive dimensions and use them to compute the connected and irreducible components of a complex algebraic variety. If the variety is given by polynomials of degree ≤ d in n variables, then our algorithms run in parallel (sequential) time (n log d)O(1) (dO(n 4)). In the case of a hypersurface the complexity drops to O(n log d) (dO(n)). In th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- The American Mathematical Monthly
دوره 113 شماره
صفحات -
تاریخ انتشار 2006