2023/03/01 by Towers, David A., Ciloglu, Zekiye
#17B05 #17B20 #17B30 #17B50 #FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2303.00418
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.