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Abstract Algebra Refresher:
Review, Amplification, Examples
Thomas R. Shemanske
Contents
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Contents
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Front Matter
Colophon
Preface
1
A quick review of a first course
What is Algebra?
Partitions and Equivalence Relations
Structure-preserving maps and quotient structures
A fundamental isomorphism theorem for groups, rings, vector spaces
New algebraic objects from old: products and sums
2
Basic results in group theory
Cosets and some applications
Understanding quotients and further isomorphism theorems
Group Actions and applications
Some structure and classification theorems
The Symmetric Group
3
Basic results in ring theory
Basic definitions and motivations
Factoring in integral domains
Ideals and quotients
Euclidean domains, PIDs, UFDs and all that jazz
Identifying irreducibles
Applications
4
Definitions
Basic Definitions
Back Matter
References and Suggested Readings
Authored in PreTeXt
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Front Matter
1
A quick review of a first course
2
Basic results in group theory
3
Basic results in ring theory
4
Definitions
Back Matter
