Quasi-socle ideals in Gorenstein numerical semigroup rings

@article{Goto2007QuasisocleII,
  title={Quasi-socle ideals in Gorenstein numerical semigroup rings},
  author={Shiro Goto and Satoru Kimura and Naoyuki Matsuoka},
  journal={Journal of Algebra},
  year={2007},
  volume={320},
  pages={276-293}
}

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References

SHOWING 1-10 OF 26 REFERENCES
Links of prime ideals
Roughly speaking, a link of an ideal of a Noetherian ring R is an ideal of the form I = (z): , where z = z1, …, zg is a regular sequence and g is the codimension of . This is a very common operation
Finite homological dimension and primes associated to integrally closed ideals, II
Let I be an integrally closed ideal in a commutative Noetherian ring A. Then the local ring Ap is regular (resp. Gorenstein) for every p C AssAA/I if the projective dimension of I is finite (resp.
On ideals of finite homoloǵical dimension in local rings
  • L. Burch
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1968
In this paper I shall demonstrate certain algebraic properties of ideals of finite homological dimension in local rings. In the first section, I show that no non-zero ideal of finite homological
Links of Prime Ideals and Their Rees Algebras
Abstract In a previous paper we exhibited the somewhat surprising property that most direct links of prime ideals in Gorenstein rings are equimultiple ideals with reduction number 1. This led to the
Reductions of ideals in local rings
  • D. Northcott, D. Rees
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1954
This paper contains some contributions to the analytic theory of ideals. The central concept is that of a reduction which is defined as follows: if and are ideals and ⊆ , then is called a reduction
On the integral closure of ideals
Abstract:Among the several types of closures of an ideal I that have been defined and studied in the past decades, the integral closure has a central place being one of the earliest and most
Reduction number of links of irreducible varieties
Links of symbolic powers of prime ideals
AbstractIn this paper, we prove the following. Let $$(R, \frak{m})$$ be a Cohen-Macaulay local ring of dimension d ≥ 2. Suppose that either R is not regular or if R is regular assume that d ≥ 3. Let
Die Wertehalbgruppe eines lokalen Rings der Dimension 1
Ist R eine multiplikativ abgeschlossene Teilmenge eines diskreten Bewertungsrings V mit 1∈R,so bilden die Werte der Elemente von R eine Unterhalbgruppe H der Halbgruppe der naturlichen Zahlen N mit
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