Smarandache Neutrosophic Algebraic Structures

TL;DR

This book introduces and explores Smarandache neutrosophic algebraic structures, including groups, semigroups, loops, and N-structures, providing new definitions, properties, and generalizations in neutrosophic algebra.

Contribution

It is the first to define and analyze S-neutrosophic groups and N-groups, expanding the scope of neutrosophic algebraic structures with new concepts and properties.

Findings

Introduction of S-neutrosophic groups and N-groups

Definitions and properties of S-neutrosophic semigroups and N-semigroups

Generalizations of S-neutrosophic S-loops and groupoids

Abstract

This book has seven chapters. In Chapter one, an elaborate recollection of Smarandache structures like S-semigroups, S-loops, and S-groupoids is given. It also gives notions about N-ary algebraic stuctures and their Smarandache analogue, Neutrosophic structures viz. groups, semigroups, groupoids and loops are given in Chapter one to make the book a self-contained one. For the first time, S-neutrosophic groups and S-neutrosophic N-groups are introduced in Chapter two and their properties are given. S-neutrosophic semigroups and S-neutrosophic N-semigroups are defined and discussed in Chapter three. Chapter four defines S-neutrosophic S-loops and S-N-neutrosophic groupoids and their generalizations are given in Chapter five. Chapter six gives S-neutrosophic mixed N-structures and their duals. Chapter seven gives 68 problems for any interested reader.