User:Jshflynn/Hungerford Algebra
About
This is the coverage of the book Algebra by Thomas W. Hungerford.
$\text{I}$: Groups
$\S 1$: Semigroups, Monoids and Groups
Definition:Operation/Binary Operation
Definition:Multiplicative Notation
Definition:Product (Abstract Algebra)
Identity is only Idempotent Element in Group/Proof 2
Unique Solution of Group Equation
Equivalence of Axiom Schemata for Groups
Semigroup is Group Iff Latin Square Property Holds
Integers under Addition form Infinite Cyclic Group
Rational Numbers under Addition form Infinite Abelian Group
Real Numbers under Addition form Infinite Abelian Group
Integers under Multiplication form Countably Infinite Commutative Monoid
Rational Numbers under Multiplication form Commutative Monoid
Non-Zero Rational Numbers under Multiplication form Infinite Abelian Group
Non-Zero Real Numbers under Multiplication form Abelian Group
Integer Multiples under Multiplication form Semigroup
Definition:Symmetry Group of Square
Definition:Permutation on n Letters
Definition:Permutation on n Letters/Two-Row Notation
Definition:Group Direct Product
External Direct Product of Groups is Group
External Direct Product of Abelian Groups is Abelian Group
Order of External Direct Product
Definition:Congruence Relation
Definition:Operation Induced on Quotient Set
Quotient Structure of Monoid is Monoid
Quotient Structure of Group is Group
Quotient Structure of Abelian Group is Abelian Group
Congruence (Number Theory) is Congruence Relation
Definition:Additive Group of Integers Modulo m
Order of Additive Group of Integers Modulo m
Reduced Residue System under Multiplication forms Abelian Group
Reduced Residue System under Multiplication forms Abelian Group/Corollary
Definition:Group of Rationals Modulo One
Group of Rationals Modulo One is Group
Definition:Power of Element of Semigroup
Definition:Power of Element/Monoid
Definition:Power of Element/Group
Index Laws for Monoids/Sum of Indices
Index Laws for Monoids/Product of Indices
Natural Numbers under Addition form Commutative Monoid
Multiplicative Semigroup of Integer Multiples/Note
Mappings to Algebraic Structure form Similar Algebraic Structure
Equivalence of Axiom Schemata for Groups/Warning
Definition:Symmetry Group of Square
Reduced Residue System under Multiplication forms Abelian Group/Corollary
Modulo One is Congruence Relation on Rational Numbers
Group of Rationals Modulo One is Group
Bookmark
Even Order Group has Order 2 Element
$\S 2$
Definition:Semigroup Homomorphism
Definition:Semigroup Monomorphism
Definition:Semigroup Epimorphism
Definition:Semigroup Isomorphism
Definition:Semigroup Endomorphism
Definition:Semigroup Automorphism
Composite of Homomorphisms is Homomorphism/Algebraic Structure
Composite of Monomorphisms is Monomorphism
Composite of Epimorphisms is Epimorphism
Composite of Isomorphisms is Isomorphism
Composite of Endomorphisms is Endomorphism
Composite of Automorphisms is Automorphism
Definition:Canonical Epimorphism
Inversion Mapping is Automorphism iff Group is Abelian
Definition:Kernel of Group Homomorphism
Definition:Image of Subset under Mapping
Definition:Image Set of Mapping
Definition:Preimage of Subset under Mapping
Kernel is Trivial iff Monomorphism/Group
Definition:Closure (Abstract Algebra)/Algebraic Structure
Subgroups of Additive Group of Integers
Kernel of Group Homomorphism is Subgroup
Image of Group Homomorphism is Subgroup
Group Homomorphism Preserves Subgroups
Definition:Automorphism Group of Group
Automorphism Group is Subgroup of Symmetric Group
Intersection of Subgroups is Subgroup/General Result
Definition:Generator of Subgroup
Definition:Finitely Generated Algebraic Structure
Definition:Word (Abstract Algebra)
Integers under Addition form Infinite Cyclic Group