Fully noncentral Lie ideals and invariant additive subgroups in rings
Journal article, 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.

Author

Eusebio Gardella

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Tsiu Kwen Lee

National Taiwan University

Hannes Thiel

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Journal of the London Mathematical Society

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

Vol. 111 3 e70127

Subject Categories (SSIF 2025)

Algebra and Logic

DOI

10.1112/jlms.70127

More information

Latest update

4/3/2025 8