2024/09/05 by Eusebio Gardella, Gardella, Eusebio, Tsiu‐Kwen Lee +3 · 1 citation
Mathematics · #16W10. Secondary 16S50 #16W20 #17B60 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Operator Algebras (math.OA) #Primary 16N60 #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2409.03362
openalex publication_date 2024/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ≠ 2 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.