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 ?
A ring (R, +, *) is said to be a non-associative ring if (R, +) is an additive abelian group, (R, *) is a non-associative semigroup (i.
But RQ will only be a non-associative ring without identy.
then Q is a Loop) that the quasigroup ring RQ will be a non-associative ring with unit.
The quasigroup ring ZQ is a non-associative ring without unit element.
The smallest non-associative ring without unit is quasigroup ring given by the following example.
Clearly the quasigroup ring ZQ is a non-associative ring.
In our view groupoid rings and quasigroup rings are the rich source of non-associative SNA-rings without unit since all other rings happen to be either associative or non-associative rings with unit.
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.

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