Francesc Planas-Vilanova

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math.AC2026

Explicit minimal generating sets of a family of prime ideals with unbounded minimal number of generators in a three-dimensional power series ring

Laura GonzÃ¡lez, Francesc Planas-Vilanova

We display a new family of prime ideals with unbounded minimal number of generators in a three-dimensional power series ring over a field of characteristic zero. These primes are o…

math.AC2026★ 1 cited

Prime ideals of Moh and the characteristic of the field

Laura GonzÃ¡lez, Francesc Planas-Vilanova

We reprove and generalize a result of Moh which gives a lower bound on the minimal number of generators of an ideal in a power series ring in three variables x,y,z over a field k.…

math.AC2025

Sifted degrees of the equations of the Rees module and their connection with the Artin-Rees numbers

Philippe Gimenez, Francesc Planas-Vilanova

Let $A$ be a noetherian ring, $I$ an ideal of $A$ and $N \subset M$ finitely generated $A$ -modules. The relation type of $I$ with respect to $M$ , denoted by $rt (I; M)$ , is th…