Smarandache Semigroups

Definition: 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 included in A which is embedded with a stronger structure S. These types of structures occur in our everyday life, that’s why we study them in this book. Thus, as a particular case: A Smarandache Semigroup is a semigroup A which has a proper subset B included in A that is a group (with respect to the same binary operation on A). The main motivation and desire for writing this book, is the direct appreciation and attraction towards the Smarandache notions in general and Smarandache algebraic structures in particular. The Smarandache semigroups exhibit properties of both a group and a semigroup simultaneously. This book is a piece of work on Smarandache semigroups and assumes the reader to have a good background on group theory; we give some recollection about groups and some of its properties just for quick reference.