Integral Dependence over One-Sided Ideals, Part II: G-Left Ideals and the Köthe Problem

Masood Aryapoor

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arXiv · 2609.26909

Integral Dependence over One-Sided Ideals, Part II: G-Left Ideals and the Köthe Problem

Masood Aryapoor

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Abstract

We study integral dependence over left ideals using G-left ideals, namely left ideals maximal with respect to the failure of integrality of a fixed element. We establish several characterizations of G-left ideals, and show that their intersection is precisely the upper nilradical. Motivated by the Köthe conjecture, we introduce the class of left KI-rings as rings in which sums of left ideals integral over a fixed left ideal remain integral over that ideal. It is shown that left artinian rings, PI-rings, algebraic algebras, and algebras of dimension smaller than the cardinality of the ground field are left KI-rings.

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BibTeX RIS

Masood Aryapoor. 2026-09-22. Integral Dependence over One-Sided Ideals, Part II: G-Left Ideals and the Köthe Problem. https://arxiv.org/abs/2609.26909

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