Mastering Abstract Algebra: A Comprehensive Textbook on Groups, Rings, and Fields: Foundations and Advanced Topics in Abstract Algebra - Tapa blanda

Sinopsis

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.

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

• 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.

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