W. B. Vasantha Kandasamy
2002
The study of Smarandache Algebraic Structure was initiated in the year 1998 by Raul Padilla following a paper written by Florentin Smarandache called “Special Algebraic Structures”. In his research, Padilla treated the Smarandache algebraic structures mainly with associative binary operation. Since then the subject has been pursued by a growing number of researchers and now it would be better if one gets a coherent account of the basic and main results in these algebraic structures. This book aims to give a systematic development of the basic non-associative algebraic structures viz. Smarandache groupoids. Smarandache groupoids exhibits simultaneously the properties of a semigroup and a groupoid. Such a combined study of an associative and a non associative structure has not been so far carried out. Except for the introduction of smarandacheian notions by Prof. Florentin Smarandache such types of studies would have been completely absent in the mathematical world. Thus, Smarandache groupoids, which are groupoids with a proper subset, which is a semigroup, has several interesting properties, which are defined and studied in this book in a sequential way. This book assumes that the reader should have a good background of algebraic structures like semigroup, group etc. and a good foundation in number theory.
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