In this book, for the first time we introduce the notion of neutrosophic algebraic structures for groups, loops, semigroups and groupoids and also their neutrosophic N-algebraic structures. One is fully aware of the fact that many classical theorems like Lagrange, Sylow and Cauchy have been studied only in the context of finite groups. Here we try to shift the paradigm by studying and introducing these theorems to neutrosophic semigroups, neutrosophic groupoids, and neutrosophic loops. We have intentionally not given several theorems for semigroups and groupoid but have given several results with proof mainly in the case of neutrosophic loops, biloops and Nloops. One of the reasons for this is the fact that loops are generalizations of groups and groupoids. Another feature of this book is that only meager definitions and results are given about groupoids. But over 25 problems are suggested as exercise in the last chapter. For groupoids are generalizations of both semigroups and loops. This book has seven chapters. Chapter one provides several basic notions to make this book self-contained. Chapter two introduces neutrosophic groups and neutrosophic N-groups and gives several examples. The third chapter deals with neutrosophic semigroups and neutrosophic N-semigroups, giving several interesting results. Chapter four introduces neutrosophic loops and neutrosophic N-loops. We introduce several new, related definitions.
Hexis: Phoenix, USA
neutrosophic algebraic structures, neutrosophic logic
W.B. Vasantha Kandasamy & F. Smarandache. SOME NEUTROSOPHIC ALGEBRAIC STRUCTURES AND NEUTROSOPHIC N-ALGEBRAIC STRUCTURES. Phoenix: Hexis, 2006.
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