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Introduction to algebra
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I · Algebra basics
Chapter I.5
Complex numbers and polynomials
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I.5.1 · The field of complex numbers
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I.5.2 · Polynomial ring
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I.5.3 · Polynomial ring factorization
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I.5.4 · Field of quotients
Section I.5.1
The field of complex numbers
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Subsection I.5.1.1
Auxiliary construction
Subsection I.5.1.2
The complex plane
Subsection I.5.1.3
Geometric interpretation of operations with complex numbers
Subsection I.5.1.4
Exponentiation and root extraction
Subsection I.5.1.5
Uniqueness Theorem
Subsection I.5.1.6
Elementary geometry of complex numbers
Section I.5.2
Polynomial ring
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Subsection I.5.2.1
Polynomials in one variable
Subsection I.5.2.2
Polynomials in several variables
Subsection I.5.2.3
The division algorithm with remainder
Section I.5.3
Polynomial ring factorization
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Subsection I.5.3.1
Elementary properties of divisibility
Subsection I.5.3.2
GCD and LCM in rings
Subsection I.5.3.3
The factorial property of Euclidean rings
Subsection I.5.3.4
Irreducible polynomials
Section I.5.4
Field of quotients
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Subsection I.5.4.1
Construction of the field of fractions of an integral domain
Subsection I.5.4.2
The field of rational fractions
Subsection I.5.4.3
Elementary fractions