Weak c-ideals of Leibniz algebras

Towers, David and ÇİLOĞLU ŞAHİN, Zekiye (2023) Weak c-ideals of Leibniz algebras. Communications in Algebra, 51 (11). pp. 4676-4685. ISSN 0092-7872

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Abstract

A subalgebra B of a Leibniz algebra L is called a weak c-ideal of L if there is a subideal C of L such that L = B + C and B ∩ C ⊆ BL where BL is the largest ideal of L contained in B. This is analogous to the concept of a weakly c-normal subgroup, which has been studied by a number of authors. We obtain some properties of weak c-ideals and use them to give some characterisations of solvable and supersolvable Leibniz algebras generalising previous results for Lie algebras. We note that one-dimensional weak c-ideals are c-ideals, and show that a result of Turner classifying Leibniz algebras in which every one-dimensional subalgebra is a c-ideal is false for general Leibniz algebras, but holds for symmetric ones.