Abstract algebra

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This book is part of a series on Algebra:


This is Abstract Algebra, an advanced set of topics related to Algebra. Readers of this book are expected to have read and understand the information presented in the Algebra, and Linear Algebra books.

Contents

[edit] Abstract algebraic systems

An Abstract Algebraic System is a tuple of the form S=(\underline{S}, f_{1}, ..., f_{n}, R_{1}, ..., R_{k}, \nu). In this \underline{S} is a set, fis are function symbols of some arity , Ris are predicate symbols of some arity and ν is an interpretation of these symbols on the set.

If no predicate symbols are present then S is an Algebra (or a Universal Algebra). We allow 0-ary operations in the above, so distinguished elements must be interpreted as 0-ary operations.


[edit] Group theory

[edit] Rings

[edit] Fields

[edit] Vector Spaces

[edit] Algebras

[edit] Modules

[edit] Further abstract algebra

[edit] Authors

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