Smarandache Non-Associative Rings

By W. B. Vasantha Kandasamy

Excerpt
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.

Book Id: WPLBN0002097649
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Reproduction Date: 9/14/2011
Full Text

Title:

Smarandache Non-Associative Rings

Author:

W. B. Vasantha Kandasamy

Volume:

Language:

English

Subject:

Non-Fiction, Education, Smarandache Collections

Collection:

Authors Community

Subcollection:

Mathematics

Historic
Publication Date:

2002

Publisher:

American Research Press

Member Page:

Florentin Smarandache

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