Weak c-ideals of a Lie algebra

Towers, David and Ciloglu, Zekiye (2021) Weak c-ideals of a Lie algebra. Turkish Journal of Mathematics, 45 (5). pp. 1940-1948. ISSN 1300-0098

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Abstract

A subalgebra B of a Lie 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 weakly c-normal subgroups, 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 Lie algebras. We also note that one-dimensional weak c-ideals are c-ideals.