Results 51 to 60 of about 34,885 (140)

Dimension filtration, sequential Cohen-Macaulayness and a new polynomial invariant of graded algebras

, 2016
Let k be a field and let A be a standard N-graded k-algebra. Using numerical information of some invariants in the primary decomposition of 0 in A, namely the so-called dimension filtration, we associate a bivariate polynomial BW(A;t,w), that we call the
Goodarzi, Afshin,
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Newton-Okounkov body, Rees algebra, and analytic spread of graded families of monomial ideals

, 2023
Let $\mathcal{I} = \{I_k\}_{k \in \mathbb{N}}$ be a graded family of monomial ideal. We use the Newton-Okounkov body of $\mathcal{I}$ to: (a) give a characterization for the Noetherian property of the Rees algebra of the family; and (b) present a ...
Ha, Huy Tai, Nguyen, Thai Thanh
core  

Ideal theory in semirings

, 1967
A semiring is a non-empty set on which there are defined two associative binary operations, called addition and multiplication, such that multiplication distributes over addition both from the left and from the right. A non-empty subset I in a semiring R
Allen, Paul Jentry
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Hilbert coefficients and the Gorenstein property of the associated graded ring

, 2004
In this article we investigate the Gorenstein property of the associated graded ring GA(I) of an ideal I in a Gorenstein local ring (A,m) of positive dimension. We especially concentrate on the case where I is m-primary. Assuming that the Rees algebra of
Tarmo Järvilehto, Eero Hyry, Järvilehto, Tarmo, Hyry, Eero   +3 more
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Degree functions and projectively full ideals in 2-dimensional rational singularities that can be desingularized by blowing up the unique maximal ideal

, 2010
Let (R,m) be a 2-dimensional rational singularity with algebraically closed residue field and for which the associated graded ring is an integrally closed domain. According to Göhner, (R,m) satisfies condition (N): given a prime divisor v, there exists a
Van Lierde, Veronique
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Length One Ideal Extensions And Their Associated Graded Rings

, 2007
Let (R; m) be a d-dimensional Cohen-Macaulay local ring. Given m-primary ideals J I of R such that I is contained in the integral closure of J and (I=J) = 1, we compare depth G(J) and depth G(I).
Sam Huckaba
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Cohen–Macaulayness and negativity of A-invariants in Rees algebras associated to m-primary ideals of minimal multiplicity

, 2000
Let I be an m-primary ideal in a Cohen–Macaulay local ring (A,m) of d=dimA≥1. The ideal I is said to have minimal multiplicity if μA(I)=eI(A)+d−ℓA(A/I).
Goto, Shiro
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Stable ideals in Gorenstein local rings

, 1990
Let (R,m) be a Gorenstein local ring. We give a criterion for a stable m-primary ideal of R to have the Gorenstein associated graded ring.
Ooishi, Akira
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Tight closure of finite length modules in graded rings

, 2006
In this article, we look at how the equivalence of tight closure and plus closure (or Frobenius closure) in the homogeneous m-coprimary case implies the same closure equivalence in the nonhomogeneous m-coprimary case in standard graded rings.
Dietz, Geoffrey D.
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Local cohomology of Rees algebras and Hilbert functions

, 1995
Let I be an ideal primary to the maximal ideal in a local ring. We utilize two well-known theorems due to J.-P. Serre to prove that the difference between the Hilbert function and the Hilbert polynomial of I is the alternating sum of the graded pieces of
Jugal Verma, Bernard Johnston
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