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.
References in periodicals archive ?
In analogy to the doubling of vector spaces introduced for the [L.sub.[infinity]] realization of Theorem 1 we will show that every nonassociative algebra has a realization as an [A.sub.[infinity]] algebra.
Let (V,*) be a nonassociative algebra and [V.sup.*] a vector space isomorphic to V with the isomorphism denoted by V [contains as member of] a [??] [a.sup.*] [member of] [V.sup.*].
This completes the proof that any nonassociative algebra can be embedded into an [A.sub.[infinity]] algebra.
By defining a new binary operation a-b = (1/2)(ab + ba) on an associative algebra over a field whose characteristic is not equal to 2, we obtain another important nonassociative algebra known as Jordan algebra.
Moreover, we introduce a new class of a nonassociative algebra called left almost algebra.
The Role of Nonassociative Algebra in Projective Geometry
Maltsev used the name "Moufang-Lie algebras" for these nonassociative algebras while Sagle [8] introduced the term "Malcev algebras." Equivalent defining identities of Maltsev algebras are pointed out in [8].
Nonassociative Algebras in Physics, Hadronic Press, Palm Harbor 1994; ActaAppl.
Nonlinear Elliptic Equations and Nonassociative Algebras
Nadirashvili, Tkachev, and Vladut present students, academics, and mathematicians with a collection of applications of noncommutative and nonassociative algebras, used to construct unusual solutions to nonlinear elliptic partial differential equations of the second order.
The original motivation to introduce the class of nonassociative algebras known as Jordan algebras came from quantum mechanics (see [?]).