nonassociative algebra

nonassociative algebra

[‚nän·ə¦sō·shəd·əv ′al·jə·brə] (mathematics) A generalization of the concept of an algebra; it is a nonassociative ring R which is a vector space over a field F satisfying a (xy) = (ax) y = x (ay) for all a in F and x and y in R.