Enveloping algebras that are principal ideal rings

@article{Siciliano2017EnvelopingAT,
title={Enveloping algebras that are principal ideal rings},
author={S. Siciliano and H. Usefi},
journal={Journal of Pure and Applied Algebra},
year={2017},
volume={221},
pages={2573-2581}
}

Let L be a restricted Lie algebra over a field of positive characteristic. We prove that the restricted enveloping algebra of L is a principal ideal ring if and only if L is an extension of a finite-dimensional torus by a cyclic restricted Lie algebra.