Reducibility by polynomial functions
We study the preorder $\le_p$ on the family of subsets of an algebraically closed field of characteristic $0$ defined by letting $A\le_pB $ if there exists a polynomial $P$ such that $A=P^{-1}(B)$.
math.AC↗
arXiv subjects
Carla Massaza
Publications and source records attributed to Carla Massaza.
On the Intermediate Value Theorem over a Valued Field
The paper proves the intermediate value theorem for polynomials and power series over a valued field with divisible valuation group and infinite residue field. Some further results on the behaviour of the valuation are obtained using Hensel's Lemma.
math.AC↗
Double series over a non-Archimedean field
In the present paper we investigate the convergence of a double series over a complete non-Archimedean field and prove that, while the proofs are somewhat different, the Archimedean results hold true.
math.CA↗
Strongly inessential elements of a perfect height 2 ideal
In this paper we expand on some results exposed in a previous one, in which we introduced the concept of inessential and strongly inessential generators in a standard basis of a saturated homogeneous ideal. The appearance of strongly inessential elements seemed to be a non generic situation; in this paper we analyze their presence in a perfect height 2 ideal with the greatest number of generators, according to Dubreil's inequality.
math.AC↗
Essential and inessential elements of a standard basis
In this paper we introduce the concept of inessential element of a standard basis of I, where I is any homogeneous ideal of a polynomial ring. An inessential element is, roughly speaking, a form of the basis whose omission produces an ideal having the same saturation of I; it becomes useless in any dehomogenization of I with respect to a linear form. We study the properties of the basis linked to the presence of inessential elements and give some examples.
math.AC↗