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Introduction to algebra
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I · Algebra basics
Chapter I.4
Groups. Rings. Fields.
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I.4.1 · Sets with algebraic operations
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I.4.2 · Groups.
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I.4.3 · Rings and fields
Section I.4.1
Sets with algebraic operations
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Subsection I.4.1.1
Binary operations
Subsection I.4.1.2
Semigroups and monoids
Subsection I.4.1.3
Generalized associativity; powers
Subsection I.4.1.4
Invertible elements
Section I.4.2
Groups.
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Subsection I.4.2.1
Definition and examples
Subsection I.4.2.2
Cyclic groups
Subsection I.4.2.3
Isomorphisms
Subsection I.4.2.4
Homomorphisms
Subsection I.4.2.5
Glossary. Examples
Section I.4.3
Rings and fields
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Subsection I.4.3.1
Definition and general properties of rings
Subsection I.4.3.2
Congruences. The ring of residue classes
Subsection I.4.3.3
Ring homomorphisms
Subsection I.4.3.4
Types of rings. Field
Subsection I.4.3.5
Field characteristic
Subsection I.4.3.6
Note on linear systems