# User:Jshflynn/Howson Handbook

## If you would like to take over

I have to stop doing this for a week so I'm turning off the log in page for me. If anyone would like to take over, here you go:

### The List

+ Chapter 4: Number Systems I

Definition:Natural Number

++ Peano's Axioms

Definition:Successor Mapping on Natural Numbers

Axiom:Peano's Axioms

Principle of Mathematical Induction

Definition by Induction of Natural Number Addition

Definition:Multiplication/Natural Numbers/Minimal Infinite Successor Set

Definition:Inequality

Definition:Trichotomy

Definition:Relation Compatible with Operation

Definition:Well-Ordering/Definition 1

Definition:Ordered Set

Definition:Totally Ordered Set

++ A Set-Theoretic Approach

Definition:Set Equivalence

Definition:Cardinality

Definition:Cardinal

Definition:Cardinal Number

Definition:Zero (Cardinal)

Definition:One (Cardinal)

Definition:Sum of Cardinals

Definition:Product of Cardinals

Definition:Cardinal Exponentiation

Definition:Finite Set

Definition:Infinite Set

Definition:Finite Cardinal

Definition:Infinite Cardinal

Natural Numbers as Cardinals

Definition:Ordinal/Transfinite

Definition:Countable Set/Definition 1

Definition:Uncountable Set

Continuum Hypothesis

++ The Rational Integers

Definition:Integer

Definition:Multiplication/Integers

Definition:Negative/Integer

Definition:Positive/Integer

++ The Rational Numbers

Definition:Rational Number

Definition:Multiplication/Rational Numbers

+ Chapter 5: Groups I

Definition:Group

Definition:Multiplicative Notation

Definition:Identity (Abstract Algebra)/Two-Sided Identity

Definition:Inverse (Abstract Algebra)/Inverse

Definition:Semigroup

Definition:Monoid

Definition:Magma

Definition:Abelian Group

Definition:Finite Group

Definition:Order of Structure

Definition:Order of Group Element

Definition:Infinite Group

Definition:P-Group

Definition:Periodic Group

Definition:Aperiodic Group

Definition:Cyclic Group

Definition:Power of Element/Group

Definition:Generator of Group

Definition:Group of Permutations

Definition:Symmetric Group

Definition:Alternating Group

Definition:Symmetry Group

Definition:Dihedral Group

++ Subgroups

Definition:Subgroup

Definition:Proper Subgroup

Definition:Permutation Group

Definition:Coset/Left Coset

Definition:Coset/Right Coset

Definition:Index of Subgroup

Definition:Normal Subgroup/Definition 1

++ Chapter 6: Rings and Fields

Definition:Ring

Definition:Ring with Unity

Definition:Commutative Ring

Definition:Subring

Definition:Unit of Ring

Definition:Group of Units

Definition:Division Ring

Definition:Field

Definition:Subfield

Definition:Ordered Ring

Positive Elements of Ordered Ring

Definition:Integral Domain

Definition:Zero Divisor

Definition:Zero Divisor/Ring

Definition:Characteristic (Ring Theory)

Definition:Ideal (Ring Theory)

Definition:Left Ideal

Definition:Right Ideal

Definition:Maximal Ideal

Definition:Subset Product

Definition:Principal Ideal

Definition:Generator of Ideal

Definition:Principle Ideal Domain

Definition:Greatest Common Divisor/Integral Domain

Definition:GCD Domain

Definition:Coprime/GCD Domain

Definition:Lowest Common Multiple/Integral Domain

Definition:Irreducible (Ring Theory)

Definition:Associate/Commutative Ring

Definition:Unique Factorization Domain

+ Chapter 7: Homomorphisms and Quotient Algebras

Definition:Homomorphism (Abstract Algebra)

Definition:Group Homomorphism

Definition:Ring Homomorphism

Definition:Monomorphism (Abstract Algebra)

Definition:Epimorphism (Abstract Algebra)

Definition:Isomorphism (Abstract Algebra)

Definition:Endomorphism

Definition:Automorphism (Abstract Algebra)

Definition:Homomorphism (Abstract Algebra)/Image

Definition:Kernel of Group Homomorphism

Definition:Exact Sequence

Definition:Short Exact Sequence

Definition:Quotient Group

Definition:Quotient Ring

Definition:Quotient Field