  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).
