منابع مشابه
Initial Ideals of Truncated Homogeneous Ideals
Denote by R the power series ring in countably many variables over a eld K; then R 0 is the smallest sub-algebra of R that contains all homogeneous elements. It is a fact that a homogeneous, nitely generated ideal J in R 0 have an initial ideal gr(J), with respect to an arbitrary admissible order, that is locally nitely generated in the sense that dimK gr(J) d P d?1 j=1 R 0 j gr(J) d?j < 1 for ...
متن کاملBorel Fixed Initial Ideals of Prime Ideals in Dimension Two
We prove that if the initial ideal of a prime ideal is Borel-fixed and the dimension of the quotient ring is less than or equal to two, then given any non-minimal associated prime ideal of the initial ideal it contains another associated prime ideal of dimension one larger. Let R = k[x1, x2, . . . , xr] be a polynomial ring over a field. We will say that an ideal I ⊆ R has the saturated chain p...
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 کاملOn ideals of ideals in $C(X)$
In this article, we have characterized ideals in $C(X)$ in which every ideal is also an ideal (a $z$-ideal) of $C(X)$. Motivated by this characterization, we observe that $C_infty(X)$ is a regular ring if and only if every open locally compact $sigma$-compact subset of $X$ is finite. Concerning prime ideals, it is shown that the sum of every two prime (semiprime) ideals of e...
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 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 Commutative Algebra
سال: 2020
ISSN: 1939-2346
DOI: 10.1216/jca.2020.12.91