Work

Fully noncentral Lie ideals and invariant additive subgroups in rings

Year: 2025

Type: article

Abstract: We prove conditions ensuring that a Lie ideal or an invariant additive subgroup in a ring contains all additive commutators. A crucial assumption is that the subgroup is fully noncentral, that is, its image in every quotient is noncentral. For a unital algebra over a field of characteristic where every additive commutator is a sum of square‐zero elements, we show that a fully noncentral subspace is a Lie ideal if and only if it is invariant under all inner automorphisms. This applies in particular to zero‐product balanced algebras.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70127

Authors: Eusebio Gardella, Tsiu‐Kwen Lee, Hannes Thiel

Institutions: Chalmers University of Technology, University of Gothenburg, National Taiwan University

Language: English

Topic: Rings, Modules, and Algebras

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funders: Knut och Alice Wallenbergs Stiftelse, Vetenskapsrådet