Mastering Abstract Algebra: A Comprehensive Textbook on Groups, Rings, and Fields: Foundations and Advanced Topics in Abstract Algebra
Looking to master abstract algebra for your degree—and beyond?
Whether you're an undergraduate student, a mathematics enthusiast, or preparing for Ph.D. entrance exams and competitive tests like CSIR-NET, GATE, SET, or university-level M.Sc. & Ph.D. entrance exams, this textbook is designed to help you succeed.
Mastering Abstract Algebra delivers a clear, structured, and modern approach to the key areas of group theory and ring theory, building both strong theoretical understanding and exam readiness.
📘 What’s Inside:
Unit I – Foundations of Group Theory (22 Lectures)
Definitions and core properties of Groups and Subgroups
Explore Cyclic Groups, Permutation Groups, and Cosets
Step-by-step explanation of Lagrange’s Theorem
Unit II – Group Morphisms and Structure (23 Lectures)
Understand Group Homomorphisms and Cayley’s Theorem
Study Normal Subgroups, Quotient Groups, and key structural results
Learn the Fundamental Theorems of Homomorphism with clarity
Unit III – Rings, Fields, and Algebraic Structures
Definitions and properties of Rings, Subrings, Integral Domains, and Fields
Study Ring Morphisms and the Characteristic of Rings and Fields
Build a strong base for advanced algebra and number theory
🏆 Why This Book?
Ideal for Ph.D. Entrance Exams and advanced studies
Covers essential theory for MCQ-based tests like CSIR-NET, GATE, SET
Written in a modern, student-friendly style
Suitable for classroom use, self-study, or exam preparation
Includes foundational material for those planning to pursue research in mathematics
If you're aiming for academic excellence or preparing to take your mathematical journey to the research level, this textbook is your trusted companion.