nonassociative algebra

Let $k$ be a commutative unital ring, usually a field.

A **nonassociative $k$-algebra** is a $k$-module $V$ equipped with a bilinear product $V\otimes V\to V$.

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 July 20, 2010 00:33:35
by Toby Bartels
(64.89.48.241)