Year: 2026
Type: preprint
Abstract: We establish strong and explicit forms of a one-sided Nullstellensatz for polynomial rings D[x1, . . . , xn] over arbitrary division rings D with central indeterminates. To this end, we employ the theory of integral dependence over left ideals and the notion of G-left ideals, which plays a role analogous to that of G-ideals in the classical theory. We prove that the Jacobson radical of any left ideal of D[x1, . . . , xn] coincides with the intersection of all G-left ideals containing it. As a consequence, we obtain an explicit description of Jacobson radicals of left ideals of polynomial rings over division rings in terms of integral dependence.
Source: arXiv (Cornell University)
Author: Aryapoor, Masood
Institution: Mälardalen University
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214798403