## Smarandache Non-Associative Rings

**Authors:** W. B. Vasantha Kandasamy

An associative ring is just realized or built using reals or complex; finite or infinite
by defining two binary operations on it. But on the contrary when we want to define
or study or even introduce a non-associative ring we need two separate algebraic
structures say a commutative ring with 1 (or a field) together with a loop or a
groupoid or a vector space or a linear algebra. The two non-associative well-known
algebras viz. Lie algebras and Jordan algebras are mainly built using a vector space
over a field satisfying special identities called the Jacobi identity and Jordan identity
respectively. Study of these algebras started as early as 1940s. Hence the study of
non-associative algebras or even non-associative rings boils down to the study of
properties of vector spaces or linear algebras over fields.

**Comments:** 201 pages

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### Submission history

[v1] 7 Mar 2010

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