Smarandache Non-Associative Rings
W. B. Vasantha Kandasamy
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 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 in 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 in R, that is an associative ring (with respect to the same binary operations on R).
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 in 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 in R, that is an associative ring (with respect to the same binary operations on R).
Catégories:
Année:
2002
Editeur::
American Research Press
Langue:
english
Pages:
151
ISBN 10:
1931233691
ISBN 13:
9781931233699
Fichier:
PDF, 823 KB
IPFS:
,
english, 2002