## Ideals of Herzog–Northcott type

- L. O'Carroll, F. Planas-Vilanova
- MathematicsProceedings of the Edinburgh Mathematical Society
- 29 January 2010

Abstract This paper takes a new look at ideals generated by 2×2 minors of 2×3 matrices whose entries are powers of three elements not necessarily forming a regular sequence. A special case of this is… Expand

## Degree and Algebraic Properties of Lattice and Matrix Ideals

- L. O'Carroll, F. Planas-Vilanova, R. Villarreal
- MathematicsSIAM Journal on Discrete Mathematics
- 21 March 2013

We study the degree of nonhomogeneous lattice ideals over arbitrary fields, and give formulas to compute the degree in terms of the torsion of certain factor groups of $\mathbb{Z}^s$ and in terms of… Expand

## Rings of weak dimension one and syzygetic ideals

- F. Planas-Vilanova
- Mathematics
- 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.

## Degree and algebraic properties of lattice and binomial matrix ideals

- L. O'Carroll, F. Planas-Vilanova, R. Villarreal
- Mathematics
- 21 March 2013

## On the module of effective relations of a standard algebra

- F. Planas-Vilanova
- MathematicsMathematical Proceedings of the Cambridge…
- 1 September 1998

Let A be a commutative ring. We denote by a standard A-algebra a commutative graded A-algebra U=[oplus ]n[ges ]0Un with U0=A and such that U is generated as an A-algebra by the elements of U1. Take x… Expand

## The equations of Rees algebras of equimultiple ideals of deviation one

- F. Muiños, F. Planas-Vilanova
- Mathematics
- 20 March 2012

We describe the equations of the Rees algebra R(I) of an equimultiple
ideal I of deviation one provided that I has a reduction generated
by a regular sequence x1, . . . , xs such that the initial… Expand

## Sally’s question and a conjecture of shimoda

- S. Goto, L. O'Carroll, F. Planas-Vilanova
- MathematicsNagoya mathematical journal
- 4 September 2012

Abstract In 2007, Shimoda, in connection with a long-standing question of Sally, asked whether a Noetherian local ring, such that all its prime ideals different from the maximal ideal are complete… Expand

## Regular local rings of dimension four and Gorenstein syzygetic prime ideals

- F. Planas-Vilanova
- MathematicsJournal of Algebra
- 19 May 2021

## Noetherian rings of low global dimension and syzygetic prime ideals

- F. Planas-Vilanova
- MathematicsJournal of Pure and Applied Algebra
- 3 October 2019

## The primary components of positive critical binomial ideals

- L. O'Carroll, F. Planas-Vilanova
- Mathematics
- 29 June 2012

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