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 ?
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, [Z.sub.2]Q is a non-associative ring without unit.
Obviously RQ is a non-associative ring. As Q is a Smarandache quasigroup Q contains a group G properly.
Clearly the quasigroup ring ZQ is a non-associative ring. Consider the subset S = {1, 2, 3, 4} then S is a group and hence ZS is a group ring and hence also a quasigroup ring.
Keywords Non-associative rings; Smarandache non-associative rings; Quasigroups; Smarandache quasigroups; Smarandache quasigroup rings.
This structure provides number of examples of SNA-rings (Smarandache non-associative rings).
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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