Rings of weak dimension one and syzygetic ideals

@inproceedings{PlanasVilanova1996RingsOW,
  title={Rings of weak dimension one and syzygetic ideals},
  author={Francesc Planas-Vilanova},
  year={1996}
}
. We prove that rings of weak dimension one are the rings with all (three-generated) ideals syzygetic. This leads to a characterization of these rings in terms of the Andr(cid:19)e-Quillen homology. 

Some Applications of André–Quillen Homology to Classes of Arithmetic Rings

We compute the first André–Quillen homology modules for the simple over-rings of integrally closed domains and study an ideal theoretic condition arising from the vanishing of H 1.

Noetherian rings of low global dimension and syzygetic prime ideals

TWO-GENERATED IDEALS OF LINEAR TYPE

We show that in a local S1 ring every two-generated ideal of linear type can be generated by a two-element sequence of linear type and give an exam- ple which illustrates that the S1 condition is

The strong uniform Artin-Rees property in codimension one

The purpose of this paper is to prove the following theorem of uniform Artin-Rees properties: Let $A$ be an excellent (in fact J-2) ring and let $N\subset M$ be two finitely generated $A$-modules

Torsion freeness of symmetric powers of ideals

Let I be an ideal in a Noetherian commutative ring R with unit, let k > 2 be an integer, and let αk i S k I → I k be the canonical surjective R-module homomorphism from the kth symmetric power of I

The strong uniform Artin-Rees property in codimension one

This result is a variation of a theorem of Duncan and O Carroll DO maximal ideals are replaced by any ideal using the unavoidable hypothesis dim M N as an example of Wang shows W Moreover it provides

Formally regular rings and descent of regularity

. Valuation rings and perfectoid rings are examples of (usually nonnoetherian) rings that behave in some sense like regular rings. We give and study an extension of the concept of regular local rings

References

SHOWING 1-7 OF 7 REFERENCES

Arithmetic of Blowup Algebras

1. Krull dimension 2. Syzygetic sequences 3. Approximation complexes 4. Linkage and Koszul homology 5. Arithmetic of Rees algebras 6. Factoriality 7. Ideal transforms 8. The equations of Rees

Ideals de tipus lineal i homologia d'André-Quillen

EL TRABAJO TIENE COMO OBJETIVO EL ESTUDIO DE LOS IDEALES DE TIPO LINEAL, ES DECIR, DE LOS IDEALES CON ALGEBRA DE REES SIMETRICA, SE DAN DIVERSAS CARACTERIZACIONES HOMOLOGICAS DE LA CONDICION TIPO