Fully noncentral Lie ideals and invariant additive subgroups in rings
Artikel i vetenskaplig tidskrift, 2025

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 (Formula presented.) 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.

Författare

Eusebio Gardella

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Tsiu Kwen Lee

National Taiwan University

Hannes Thiel

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Publicerad i

Journal of the London Mathematical Society

0024-6107 (ISSN) 1469-7750 (eISSN)

Vol. 111 Nummer/häfte 3 art. nr e70127

Kategorisering

Ämneskategorier (SSIF 2025)

Algebra och logik

Identifikatorer

DOI

10.1112/jlms.70127

Mer information

Senast uppdaterat

2025-04-03