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Introduction to algebra
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III · Main algebraic structures
Chapter III.4
Rings and modules
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On this page
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III.4.1 · Ring-theoretic constructions
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III.4.2 · Individual results about rings
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III.4.3 · Modules.
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III.4.4 · Algebras over a field
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III.4.5 · Irreducible modules over a Lie algebra 51(2)
Section III.4.1
Ring-theoretic constructions
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Subsection III.4.1.1
Ring ideals and quotient rings
Subsection III.4.1.2
The splitting field of a polynomial
Subsection III.4.1.3
Ring Isomorphism Theorems
Section III.4.2
Individual results about rings
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Subsection III.4.2.1
Gaussian integers
Subsection III.4.2.2
The canonical decomposition of the sum of two squares
Subsection III.4.2.3
Polynomial extensions of factorial rings
Subsection III.4.2.4
The structure of the multiplicative group
U
(
Z
n
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U(Z_n)
U
(
Z
n
)
Section III.4.3
Modules.
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Subsection III.4.3.1
Initial information about modules
Subsection III.4.3.2
Free modules
Subsection III.4.3.3
Integer elements of the ring
Section III.4.4
Algebras over a field
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Subsection III.4.4.1
Definitions and examples of algebras
Subsection III.4.4.2
Division algebras
Subsection III.4.4.3
Group algebras and modules over them
Section III.4.5
Irreducible modules over a Lie algebra 51(2)
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Subsection III.4.5.1
Original material
Subsection III.4.5.2
Weights and multiplicities
Subsection III.4.5.3
Leading vector
Subsection III.4.5.4
Classification result