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April 21, 2026, 11:36 p.m.
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NOTE
SOURCE: Hien M. Abstract Algebra. Suitable for Self-Study or Online Lectures 2024
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COVER
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MEDIAINFO
Textbook in PDF format
This book contains the basics of abstract algebra.
In addition to elementary algebraic structures such as groups, rings and solids, Galois theory in particular is developed together with its applications to the cyclotomic fields, finite fields or the question of the resolution of polynomial equations.
Special attention is paid to the natural development of the contents. Numerous intermediate explanations support this basic idea, show connections and help to better penetrate the underlying concepts.
The book is therefore particularly suitable for learning algebra in self-study or accompanying online lectures.
Preface
Motivation and Prerequisites
Field Extensions and Algebraic Elements
Groups
Group Quotients and Normal Subgroups
Rings and Ideals
Euclidean Rings, Principal Ideal Rings, Noetherian Rings
Unique Factorization Domains
Quotient Fields for Domains
Irreducible Polynomials in UFDs
Galois Theory (I)—Theorem A and Its Variant A’
Intermezzo: An Explicit Example X5 – 777X + 7
Normal Field Extensions
Separability
Galois Theory (II)—The Fundamental Theorem
Cyclotomic Fields
Finite Fields
More Group Theory—Group Actions and Sylow's Theorems
Solvability of Polynomial Equations
Proof of the Existence of an Algebraic Closure
Tricks and Methods to Classify Groups of a Given Order
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