  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 which is
embedded with a stronger structure S. By proper subset one understands a set
included in A, different from the empty set, from the unit element if any, and
from A. These types of structures occur in our every day's life, that's why we
study them in this book.
  Thus, as three particular cases:
  1) A Smarandache semiring is a semiring A such that a proper subset B of A is
a semifield (with respect to the same induced operation). 2) A Smarandache
semifield is a semifield A such that a proper subset B of A is a k-semi
algebra, with respect to the same induced operations and an external operator.
3) A Smarandache semivector space is a semivector space A (over a semifield B)
which is a Smarandache semigroup.
