منابع مشابه
Generic Gaussian ideals
The content of a polynomial f(t) is the ideal generated by its coefficients. Our aim here is to consider a beautiful formula of Dedekind–Mertens on the content of the product of two polynomials, to explain some of its features from the point of view of Cohen–Macaulay algebras and to apply it to obtain some Noether normalizations of certain toric rings. Furthermore, the structure of the primary ...
متن کاملGaussian Polynomials and Content Ideals
We prove that every regular Gaussian polynomial over a locally Noetherian ring has invertible content ideal. We do this by first proving that Gaussian polynomials over an approximately Gorenstein local ring have principal content ideal. We also show over locally Noetherian rings that a regular polynomial f of degree n is Gaussian if c(fg) = c(f)c(g) for polynomials g of degree at most n. Introd...
متن کاملReverse Lexicographic Initial Ideals of Generic Ideals Are Nitely Generated
This article generalizes the well-known notion of generic forms to the algebra R 0 , introduced in 27]. For the total degree, then reverse lexicographic order, we prove that the initial ideal of an ideal generated by nitely many generic forms (in countably innnitely many variables) is nitely generated. This contrasts to the lexicographic order, for which initial ideals of generic ideals in gene...
متن کاملGeneric initial ideals of points and curves
Let I be the defining ideal of a smooth irreducible complete intersection space curve C with defining equations of degrees a and b. We use the partial elimination ideals introduced by Mark Green to show that the lexicographic generic initial ideal of I has Castelnuovo-Mumford regularity 1+ ab(a− 1)(b− 1)/2 with the exception of the case a = b = 2, where the regularity is 4. Note that ab(a− 1)(b...
متن کاملSaturation Properties of Ideals in Generic Extensions
We consider saturation properties of ideals in models obtained by forcing with countable chain condition partial orderings. As sample results, we mention the following. If M[G] is obtained from a model M of GCH via any a-finite chain condition notion of forcing (e.g. add Cohen reals or random reals) then in M[G] every countably complete ideal on <o, is <o3-saturated. If "o-finite chain conditio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1998
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(97)80001-1