# Variety of Lie rings

From Groupprops

## Definition

### As a plain variety

The variety of Lie rings is the variety of algebras with the operator domain consisting of:

- A binary operation
- A unary operation (prefix symbol)
- A constant
- A binary operation

such that the following universal identities are satisfied:

The identities (1)-(4) say that we get an Abelian group under , the identities (5) and (6) say the Lie bracket is bilinear, the identity (7) says it is alternating, and the identity (8) is the Jacobi identity.

## Properties

A complete listing of the universal algebra-theoretic properties of Lie rings is available at:

Category:Property satisfactions for the variety of Lie rings