Chief factors covered by projectors of soluble Leibniz algebras

TL;DR

This paper proves that in soluble Leibniz algebras, a projector covers a chief factor if and only if that factor is F-central, clarifying the relationship between projectors and F-centrality.

Contribution

It establishes the converse of a known result, showing that covering a chief factor implies F-centrality in soluble Leibniz algebras.

Findings

If a projector covers a chief factor, then the factor is F-central.

The converse of the known implication is proven.

Provides a characterization of chief factors covered by projectors.

Abstract

Let F be a saturated formation of soluble Leibniz algebras. Let K be an F-projector and A/B a chief factor of the soluble Leibniz algebra L. It is well-known that if A/B is F-central, then K covers A/B. I prove the converse: if K covers A/B, then A/B is F-central.