Smarandache Non-Associative Rings
Abstract
Description
Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a proper subset B contained in A which is embedded with a stronger structure S. These types of structures occur in our everyday's life, that's why we study them in this book.
Thus, as a particular case:
A non-associative ring is a non-empty set R together with two binary operations '+' and '.' such that (R, +) is an additive abelian group and (R, .) is a groupoid. For all a, b, c belonging to R we have (a + b) . c = a . c + b . c and c . (a + b) = c . a + c . b. A Smarandache non-associative ring is a non-associative ring (R, +, .) which has a proper subset P contained in R, that is an associative ring (with respect to the same binary operations on R).
150 pages, several new definitions, 44 tables and 150 problems
150 pages, several new definitions, 44 tables and 150 problems