  In this book, we introduce the notion of Smarandache special definite
algebraic structures. We can also call them equivalently as Smarandache
definite special algebraic structures. These new structures are defined as
those strong algebraic structures which have in them a proper subset which is a
weak algebraic structure. For instance, the existence of a semigroup in a group
or a semifield in a field or a semiring in a ring. It is interesting to note
that these concepts cannot be defined when the algebraic structure has finite
cardinality i.e., when the algebraic structure has finite number of elements in
it.
  This book has four chapters. Chapter one is introductory in nature. In
chapter two, the notion of Smarandache special definite groups and Smarandache
special definite fields are introduced and several interesting properties are
derived. The notion of Smarandache definite special rings, vector spaces and
linear algebras are introduced and analyzed in chapter three. The final chapter
suggests over 200 problems.
