nonassociative algebra

(redirected from Non-associative algebra)
Also found in: Wikipedia.

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.
References in periodicals archive ?
Thirty-three papers from the July 2003 conference on non-associative algebra held in Mexico present recent results in non-associative rings and algebras, quasigroups and loops, and their application to differential geometry and relativity.
Giambruno and Zaicey show how to combine methods of ring theory, combinatorics and representation theory of groups with an analytical approach to study the polynomial identities satisfied by a given algebra, In the process they describe such topics as polynomial identities and PI-algebras, Sn-representations, group gradings and group actions, codimentation and colength growth, matrix invariants and central polynomials, the PI-exponent of an algebra, polynomial growth the low PI-exponent, classifying minimal variables, computing the exponent of a polynomial, G-identities and related action, superalgebras, 8-algebras and codimension growth, Lie algebras and non-associative algebras, and in an appendix, the generalized six-square theorem.

Full browser ?