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Neutrosophic Bilinear Algebras and Their Generalizations

By Smarandache, Florentin

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Book Id: WPLBN0002828464
Format Type: PDF eBook:
File Size: 4.04 MB
Reproduction Date: 7/31/2013

Title: Neutrosophic Bilinear Algebras and Their Generalizations  
Author: Smarandache, Florentin
Language: English
Subject: Non Fiction, Education, Algebra
Collections: Authors Community, Mathematics
Publication Date:
Publisher: World Public Library
Member Page: Florentin Smarandache


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Smarandache, B. F., & Vasantha Kandasamy, W. B. (2013). Neutrosophic Bilinear Algebras and Their Generalizations. Retrieved from

The first chapter is introductory in nature and gives a few essential definitions and references for the reader to make use of the literature in case the reader is not thorough with the basics. The second chapter deals with different types of neutrosophic bilinear algebras and bivector spaces and proves several results analogous to linear bialgebra. In chapter three the authors introduce the notion of n-linear algebras and prove several theorems related to them. Many of the classical theorems for neutrosophic algebras are proved with appropriate modifications. Chapter four indicates the probable applications of these algebraic structures. The final chapter suggests about 80 innovative problems for the reader to solve.

This book introduces the concept of neutrosophic bilinear algebras and their generalizations to n-linear algebras. This book has five chapters. The reader should be well-versed with the notions of linear algebras as well as the concepts of bilinear algebras and n- linear algebras. Further the reader is expected to know about neutrosophic algebraic structures as we have not given any detailed literature about it.

Table of Contents
Dedication 5 Preface 7 Chapter One INTRODUCTION TO BASIC CONCEPTS 9 1.1 Introduction to Bilinear Algebras and their Generalizations 9 1.2 Introduction to Neutrosophic Algebraic Structures 11 Chapter Two NEUTROSOPHIC LINEAR ALGEBRA 15 2.1 Neutrosophic Bivector Spaces 15 2.2 Strong Neutrosophic Bivector Spaces 32 2.3 Neutrosophic Bivector Spaces of Type II 50 2.4 Neutrosophic Biinner Product Bivector Space 198 Chapter Three NEUTROSOPHIC n-VECTOR SPACES 205 3.1 Neutrosophic n-Vector Space 205 3.2 Neutrosophic Strong n-Vector Spaces 276 3.3 Neutrosophic n-Vector Spaces of Type II 307 Chapter Four APPLICATIONS OF NEUTROSOPHIC n-LINEAR ALGEBRAS 359 Chapter Five SUGGESTED PROBLEMS 361 FURTHER READING 391 INDEX 396 ABOUT THE AUTHORS 402


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