Temperature coefficients for proving rings
نویسندگان
چکیده
منابع مشابه
Hilbert Coefficients and Depths of Form Rings
We present short and elementary proofs of two theorems of Huckaba and Marley, while generalizing them at the same time to the case of a module. The theorems concern a characterization of the depth of the associated graded ring of a Cohen-Macaulay module, with respect to a Hilbert filtration, in terms of the Hilbert coefficient e1. As an application, we derive bounds on the higher Hilbert coeffi...
متن کاملThe Chern Coefficients of Local Rings
The Chern numbers of the title are the first coefficients (after the multiplicities) of the Hilbert functions of various filtrations of ideals of a local ring (R, m). For a Noetherian (good) filtration A of m-primary ideals, the positivity and bounds for e1(A) are well-studied if R is Cohen-Macaulay, or more broadly, if R is a Buchsbaum ring or mild generalizations thereof. For arbitrary geomet...
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We study the problem of proving in weak theories of Bounded Arithmetic the theorem that there are arbitrarily large prime numbers. We show that the theorem can be proved by some “minimal” reasoning (i.e., in the theory I∆0) using concepts such as (the logarithm) of a binomial coefficient. In fact we prove Bertrand’s Postulate (that there is at least a prime number between n and 2n, for all n > ...
متن کاملDepth of Associated Graded Rings via Hilbert Coefficients of Ideals
Given a local Cohen-Macaulay ring (R,m), we study the interplay between the integral closedness – or even the normality – of an m-primary R-ideal I and conditions on the Hilbert coefficients of I . We relate these properties to the depth of the associated graded ring of I .
متن کاملThe Signature of the Chern Coefficients of Local Rings
This paper considers the following conjecture: If R is an unmixed, equidimensional local ring that is a homomorphic image of a Cohen-Macaulay local ring, then for any ideal J generated by a system of parameters, the Chern coefficient e1(J) < 0 is equivalent to R being non Cohen-Macaulay. The conjecture is established if R is a homomorphic image of a Gorenstein ring, and for all universally cate...
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ژورنال
عنوان ژورنال: Journal of Research of the National Bureau of Standards
سال: 1946
ISSN: 0091-0635
DOI: 10.6028/jres.037.024