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nonassociative algebra

Contents

Definition

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).

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

Examples

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

Revised on August 20, 2014 07:54:15 by Urs Schreiber (89.204.139.117)