nLab
nonassociative algebra

Let kk be a commutative unital ring, usually a field (but conceivably even a commutative rig).

A nonassociative kk-algebra is a kk-module VV equipped with a bilinear product VVVV\otimes V\to V.

This product is typically neither associative nor unital, although it can be (an example of the red herring principle).

Some interesting subclasses are Lie algebra, Jordan algebra, Leibniz algebra, alternative algebra, associative unital algebra, composition algebra

Mathematicians working in the field of nonassociative algebras often say simply ‘algebra’ meaning a nonassociative algebra.

Revised on April 29, 2014 23:23:10 by Toby Bartels (98.16.169.231)