A Short Proof of K\"othe's Conjecture for Compact Rings
Scott Goodson, Alex Taylor
TL;DR
This paper presents a new proof demonstrating that in compact rings, the upper nilradical equals the sum of all left nil ideals, utilizing properties of orthogonal idempotents.
Contribution
It offers a novel proof of K"othe's conjecture for compact rings, expanding understanding of their nilradical structure.
Findings
Upper nilradical equals sum of left nil ideals in compact rings
Utilizes properties of orthogonal idempotents in the proof
Provides a new, simplified proof of K"othe's conjecture
Abstract
We provide a new proof that the upper nilradical of a compact ring coincides with the sum of its left nil ideals using the properties of orthogonal idempotents in compact rings.
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Taxonomy
TopicsAdvanced Topics in Algebra · Rings, Modules, and Algebras · Algebraic structures and combinatorial models