nonassociative ring

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nonassociative ring

[‚nän·ə¦sō·shəd·əv ′riŋ]
(mathematics)
A generalization of the concept of a ring; it is an algebraic system with two binary operations called addition and multiplication such that the system is a commutative group relative to addition, and multiplication is distributive with respect to addition, but multiplication is not assumed to be associative.
References in periodicals archive ?
Introduction to Octonion and Other Non-Associative Algebras in Physics.
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.

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