# Metabelian Lie ring

From Groupprops

This article defines a Lie ring property: a property that can be evaluated to true/false for any Lie ring.

View a complete list of properties of Lie ringsVIEW RELATED: Lie ring property implications | Lie ring property non-implications |Lie ring metaproperty satisfactions | Lie ring metaproperty dissatisfactions | Lie ring property satisfactions | Lie ring property dissatisfactions

## Definition

No. | A Lie ring is termed metabelian if ... | A Lie ring is termed metabelian if ... |
---|---|---|

1 | its derived subring is abelian | its derived subring is an abelian Lie ring |

2 | it has an abelian ideal with abelian quotient ring | there is an abelian ideal of such that the quotient ring is abelian |

3 | its second derived subring is zero | . In other words, for all |