Smarandache Non-Associative Rings

By W. B. Vasantha Kandasamy

Book Id: WPLBN0002097649
Format Type: PDF eBook:
File Size: 0.8 MB
Reproduction Date: 9/14/2011

Title:	Smarandache Non-Associative Rings
Author:	W. B. Vasantha Kandasamy
Volume:
Language:	English
Subject:	Non-Fiction, Education, Smarandache Collections
Collections:	Mathematics, Algebra, Authors Community, Math, Political Science, Literature, Most Popular Books in China, Favorites in India, Education
Historic Publication Date:
Publisher:	American Research Press

Member Page:	Florentin Smarandache
Citation APA MLA Chicago B. Vasantha Kandasam, B. W. (n.d.). Smarandache Non-Associative Rings. Retrieved from http://www.gutenberg.cc/

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.