Set Theoretic Approach to Algebraic Structures by Vasantha Kandasamy
Set Theoretic Approach to Algebraic Structures - Table of Contents
- 1. Introduction and Basic Definitions
- 2. Sets in Semigroups and Set Subsemigroups
- 3. Set Ideals in Rings and Set Subrings
- 4. Sets in Vector Spaces & Set Subspaces
- 5. Applications of Sets to Set Codes
- 6. Further Reading and Research Bibliography
What You Will Learn in Set Theoretic Approach to Algebraic Structures
Set-Theoretic Algebraic Structures by W. B. Vasantha Kandasamy and Florentin Smarandache is an authoritative, specialized research monograph published by InfoLearnQuest that develops a novel mathematical framework extending classical algebraic structures through set-theoretic foundations. This comprehensive volume guides readers through introductory set-theoretic algebra definitions, set-theoretic structures in semigroups, set ideals in ring structures, set vector spaces, set linear transformations, and practical applications of set structures to set-based error-correcting codes with exceptional mathematical originality and analytical rigor.
Designed for research mathematicians, abstract algebraists, theoretical computer scientists, information theorists, and graduate algebraic coding researchers, this foundational text bridges abstract axiomatic set operations directly with concrete coding and communication models. Kandasamy and Smarandache detail step-by-step constructions of set semigroups, set subrings, set vector spaces over fields or sets, generator matrices for set codes, and parity-check matrix formulations. Whether you are investigating non-classical algebraic systems, developing novel error-detecting matrix codes, or exploring set-theoretic generalizations in abstract algebra, this book offers an indispensable roadmap.
Recognized globally as a pioneering contribution to modern set-theoretic algebraic generalizations, it stands as one of the best research references for understanding set semigroups, set vector spaces, and algebraic set codes. By connecting set-theoretic operations directly to structural algebra and algebraic coding theory, it serves as an essential tool for mastering set-theoretic algebraic structures with confidence.
Book Details & Specifications
Title:
Set Theoretic Approach to Algebraic Structures by Vasantha Kandasamy
Publisher:
Educational Publisher
Year:
2013
Pages:
166
Type:
PDF
Language:
English
ISBN-10 #:
B00CABFS1S
ISBN-13 #:
NA
License:
External Educational Resource
Amazon:
Amazon
About the Author: Dr. W. B. Vasantha Kandasamy
The author Dr. W. B. Vasantha Kandasamy
is a distinguished mathematician and former professor at the Indian Institute of Technology (IIT) Madras, internationally renowned for her prolific research in abstract algebra, fuzzy algebraic structures, neutrosophic logic, and algebraic coding theory. Florentin Smarandache is Professor Emeritus of Mathematics at the University of New Mexico, widely recognized for originating neutrosophic logic, paradoxism, and extensive contributions to number theory and non-classical algebraic systems.
Through Set-Theoretic Algebraic Structures, Kandasamy and Smarandache deliver a clear, systematically structured exploration of set-theoretic algebraic generalization. Their original definitions, explicit structural proofs, and practical applications to error-correcting codes make this text a classic research reference for set algebra and set-theoretic coding theory valued by mathematicians and computer scientists worldwide.
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Set Theory