Freiman $$t$$-Spread Principal Borel Ideals
نویسندگان
چکیده
An equigenerated monomial ideal $$I$$ is a Freiman if $$\mu(I^2)=\ell(I)\mu(I)-{\ell(I)\choose 2}$$ , where $$\ell(I)$$ the analytic spread of and $$\mu(I)$$ least number generators . ideals are special since there exists an exact formula computing any their powers. In this paper we give complete classification $$t$$ -spread principal Borel ideals.
منابع مشابه
Borel Ideals in Three Variables
i=1 gijXi, g = (gij) ∈ Gl(n,k)), given any term-ordering< and homogeneous ideal a ⊆ P(n), there exists a non-empty open subset U of Gl(n,k) such that as g ranges in U, gin(a) := in(g(a)) is constant. Moreover, gin(a) is fixed by the group B of upper-triangular invertible matrices, if X1 > · · · > Xn, while gin(a) is fixed by the group B′ of lower-triangular invertible matrices if X1 < · · · < X...
متن کاملThe stable set of associated prime ideals of a squarefree principal Borel ideal
It is shown that a squarefree principal Borel ideal satisfies the persistence property for the associated prime ideals. For the graded maximal ideal we compute the index of stability with respect to squarefree principal Borel ideals and determine their stable set of associated prime ideals.
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 کاملBorel homomorphisms of smooth σ-ideals
Given a countable Borel equivalence relation E on a Polish space, let IE denote the σ-ideal generated by the Borel partial transversals of E. We show that there is a Borel homomorphism from IE to IF if and only if there is a smooth-to-one Borel homomorphism from a finite index Borel subequivalence relation of E to F . As a corollary, we see that IE is homogeneous in the sense of Zapletal (2007,...
متن کاملON SPECIAL p-BOREL FIXED IDEALS
We define the reduced horseshoe resolution and the notion of conjoined pairs of ideals in order to study the minimal graded free resolution of a class of p-Borel ideals and recover Pardue’s regularity formula for them. It will follow from our technique that the graded betti numbers of these ideals do not depend on the characteristic of the base field k.
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: Mathematical Notes
سال: 2022
ISSN: ['1573-8876', '0001-4346', '1067-9073']
DOI: https://doi.org/10.1134/s0001434622070239