Year: 2023
Type: preprint
Abstract: We prove constructively a Nullstellensatz giving an equivalence between the existence of a certain kind of algebraic identity on one hand, and the impossibility of finding an increasing sequence of irreducible varieties obeying certain constraints on the other hand. The ususal Nullstellensatz corresponds to the case of varieties that are reduced to a point. We settle also a similar formal Nullstellensatz related to increasing sequences of primes. An important particular case is given by the notion of pseudo regular sequence. This allows a new characterisation of the Krull dimension of a ring. This characterisation via pseudo regular sequences is elementary and constructive. Our method uses dynamical algebraic structures which were introduced in previous papers.
Source: arXiv (Cornell University)
Author: Lombardi, Henri
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4386081259