## 7 Citations

Quasi-socle ideals in Buchsbaum rings

- MathematicsNagoya Mathematical Journal
- 2010

Abstract Quasi-socle ideals, that is, ideals of the form I = Q: m q (q ≥ 2), with Q parameter ideals in a Buchsbaum local ring (A,m), are explored in connection to the question of when I is integral…

Quasi-socle ideals in local rings with Gorenstein tangent cones

- Mathematics
- 2007

Quasi-socle ideals, that is the ideals I of the form I = Q : m q in a Noe- therian local ring (A, m) with the Gorenstein tangent cone G(m) = L n�0 m n /m n+1 are explored, where q ≥ 1 is an integer…

Stability of quasi-socle ideals

- Mathematics
- 2012

. Let A be a Noetherian local ring with maxi- mal ideal m and dim A > 0. Let G( m ) = ⊕ n ≥ 0 m n / m n +1 be the associated graded ring of m . This paper explores quasi- socle ideals in A , i.e.,…

Goto Numbers of a Numerical Semigroup Ring and the Gorensteiness of Associated Graded Rings

- Mathematics
- 2010

The Goto number of a parameter ideal Q in a Noetherian local ring (R, m) is the largest integer q such that Q: m q is integral over Q. The Goto numbers of the monomial parameter ideals of R = k[[x a…

## References

SHOWING 1-10 OF 26 REFERENCES

Links of prime ideals

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 1994

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

- Mathematics
- 2002

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

- MathematicsMathematical 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

- Mathematics
- 1994

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

- MathematicsMathematical 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

- Mathematics
- 1998

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…

Links of symbolic powers of prime ideals

- Mathematics
- 2002

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

- 1971

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…