3 citations · 9 across the 12 of their papers we have counts for
16 papers
Regular local rings of dimension four and Gorenstein syzygetic prime ideals
Francesc Planas-Vilanova
Let be a Noetherian local ring. We prove that is regular of dimension at most four if, and only if, every prime ideal, defining a Gorenstein quotient ring, is syzygetic. We…
Divisors of expected Jacobian type
Josep Àlvarez Montaner, Francesc Planas-Vilanova
Divisors whose Jacobian ideal is of linear type have received a lot of attention recently because of its connections with the theory of D-modules. In this work we are interested on…
Noetherian rings of low global dimension and syzygetic prime ideals
Francesc Planas-Vilanova
Let be a Noetherian ring. We prove that has global dimension at most two if, and only if, every prime ideal of is of linear type. Similarly, we show that has global…
Minimal free resolutions of lattice ideals of digraphs
Liam O'Carroll, Francesc Planas-Vilanova
Based upon a previous work of Manjunath and Sturmfels for a finite, complete, undirected graph, and a refined algorithm by Eröcal, Motsak, Schreyer and Steenpaß for computing syzyg…
On the integral degree of integral ring extensions
José M. Giral, Liam O'Carroll, Francesc Planas-Vilanova +1
Let be an integral ring extension of integral domains with fields of fractions and , respectively. The integral degree of , denoted by ${\rm d}_A(B)…
The relation type of affine algebras and algebraic varieties
Francesc Planas-Vilanova
We introduce the notion of relation type of an affine algebra and prove that it is well defined by using the Jacobi-Zariski exact sequence of André-Quillen homology. In particular,…