Dependency tree

An arrow runs from a page to a page that rests on it: page B points at page A when some result on A depends, through the item graph, on a result whose home is B. Only pages in Abstract Algebra are shown; anything this group rests on from elsewhere in the library is listed below.

Pages, prerequisites first

• Binary Operations, Monoids, Groups and SubgroupsExamples & counterexamples →
• Cosets, Index and Lagrange's TheoremExamples & counterexamples →
• Rings, Subrings, Integral Domains and FieldsExamples & counterexamples →
• Normal Subgroups and Quotient GroupsExamples & counterexamples →
• Group Homomorphisms and the Isomorphism TheoremsExamples & counterexamples →
• Cyclic Groups and Direct ProductsExamples & counterexamples →
• Free Groups and PresentationsExamples & counterexamples →
• Group Actions, Orbits, Stabilisers and Cayley's TheoremExamples & counterexamples →
• Ideals, Quotient Rings and the Isomorphism Theorems for RingsExamples & counterexamples →
• Divisibility, Euclidean Domains, Principal Ideal Domains and Unique FactorisationExamples & counterexamples →
• Free Products and AmalgamationExamples & counterexamples →
• Modules, Submodules, Quotient Modules and the Isomorphism TheoremsExamples & counterexamples →
• Symmetric Groups, Cycle Decomposition and the Sign HomomorphismExamples & counterexamples →
• The Fundamental Theorem of Finite Abelian GroupsExamples & counterexamples →
• Polynomial Rings, the Division Algorithm and RootsExamples & counterexamples →

Rests on other groups

• Binary Operations, Monoids, Groups and Subgroups rests on Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Relations, Functions, and Quotients, The ZFC Axioms and the Basic Set Constructions
• Cosets and Lagrange's Theorem: Examples and Counterexamples rests on Congruences, the Integers Modulo n and the Chinese Remainder Theorem, Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Divisibility, Greatest Common Divisors and Bézout's Identity, Finite Counting, Factorials and Binomial Coefficients, Foundations of the Real Numbers for Analysis, Relations, Functions, and Quotients, Roots, Rational Powers, and Classical Inequalities, The ZFC Axioms and the Basic Set Constructions
• Cosets, Index and Lagrange's Theorem rests on Congruences, the Integers Modulo n and the Chinese Remainder Theorem, Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Divisibility, Greatest Common Divisors and Bézout's Identity, Finite Counting, Factorials and Binomial Coefficients, Foundations of the Real Numbers for Analysis, Primes, Euclid's Lemma and the Fundamental Theorem of Arithmetic, Relations, Functions, and Quotients, Roots, Rational Powers, and Classical Inequalities, The ZFC Axioms and the Basic Set Constructions
• Cyclic Groups and Direct Products rests on Congruences, the Integers Modulo n and the Chinese Remainder Theorem, Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Divisibility, Greatest Common Divisors and Bézout's Identity, Finite Counting, Factorials and Binomial Coefficients, Foundations of the Real Numbers for Analysis, Relations, Functions, and Quotients, Roots, Rational Powers, and Classical Inequalities, The ZFC Axioms and the Basic Set Constructions
• Cyclic Groups and Direct Products: Examples and Counterexamples rests on Congruences, the Integers Modulo n and the Chinese Remainder Theorem, Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Divisibility, Greatest Common Divisors and Bézout's Identity, Finite Counting, Factorials and Binomial Coefficients, Relations, Functions, and Quotients, The ZFC Axioms and the Basic Set Constructions
• Divisibility, Euclidean Domains, Principal Ideal Domains and Unique Factorisation rests on Construction of the Natural Numbers, Relations, Functions, and Quotients, The ZFC Axioms and the Basic Set Constructions
• Divisibility, Euclidean Domains, Principal Ideal Domains and Unique Factorisation: Examples and Counterexamples rests on Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Divisibility, Greatest Common Divisors and Bézout's Identity, Relations, Functions, and Quotients, The ZFC Axioms and the Basic Set Constructions
• Finite Abelian Groups: Examples and Counterexamples rests on Congruences, the Integers Modulo n and the Chinese Remainder Theorem, Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Divisibility, Greatest Common Divisors and Bézout's Identity, Finite Counting, Factorials and Binomial Coefficients, Foundations of the Real Numbers for Analysis, Primes, Euclid's Lemma and the Fundamental Theorem of Arithmetic, Relations, Functions, and Quotients, Roots, Rational Powers, and Classical Inequalities, The ZFC Axioms and the Basic Set Constructions
• Free Groups and Presentations rests on Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Finite Counting, Factorials and Binomial Coefficients, Foundations of the Real Numbers for Analysis, Relations, Functions, and Quotients, Roots, Rational Powers, and Classical Inequalities, The ZFC Axioms and the Basic Set Constructions
• Free Groups and Presentations: Examples and Counterexamples rests on Congruences, the Integers Modulo n and the Chinese Remainder Theorem, Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Divisibility, Greatest Common Divisors and Bézout's Identity, Finite Counting, Factorials and Binomial Coefficients, Foundations of the Real Numbers for Analysis, Relations, Functions, and Quotients, Roots, Rational Powers, and Classical Inequalities, The ZFC Axioms and the Basic Set Constructions
• Free Products and Amalgamation rests on Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Finite Counting, Factorials and Binomial Coefficients, Foundations of the Real Numbers for Analysis, Relations, Functions, and Quotients, Roots, Rational Powers, and Classical Inequalities, The ZFC Axioms and the Basic Set Constructions
• Free Products and Amalgamation — Examples rests on Congruences, the Integers Modulo n and the Chinese Remainder Theorem, Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Divisibility, Greatest Common Divisors and Bézout's Identity, Finite Counting, Factorials and Binomial Coefficients, Relations, Functions, and Quotients, The ZFC Axioms and the Basic Set Constructions
• Group Actions, Orbits, Stabilisers and Cayley's Theorem rests on Congruences, the Integers Modulo n and the Chinese Remainder Theorem, Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Divisibility, Greatest Common Divisors and Bézout's Identity, Finite Counting, Factorials and Binomial Coefficients, Foundations of the Real Numbers for Analysis, Inclusion–Exclusion, the Pigeonhole Principle and Double Counting, Primes, Euclid's Lemma and the Fundamental Theorem of Arithmetic, Relations, Functions, and Quotients, Roots, Rational Powers, and Classical Inequalities, The ZFC Axioms and the Basic Set Constructions
• Group Actions: Examples and Counterexamples rests on Congruences, the Integers Modulo n and the Chinese Remainder Theorem, Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Divisibility, Greatest Common Divisors and Bézout's Identity, Finite Counting, Factorials and Binomial Coefficients, Foundations of the Real Numbers for Analysis, Inclusion–Exclusion, the Pigeonhole Principle and Double Counting, Primes, Euclid's Lemma and the Fundamental Theorem of Arithmetic, Relations, Functions, and Quotients, Roots, Rational Powers, and Classical Inequalities, The ZFC Axioms and the Basic Set Constructions
• Group Homomorphisms and the Isomorphism Theorems rests on Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Finite Counting, Factorials and Binomial Coefficients, Relations, Functions, and Quotients, The ZFC Axioms and the Basic Set Constructions
• Group Homomorphisms and the Isomorphism Theorems: Examples and Counterexamples rests on Congruences, the Integers Modulo n and the Chinese Remainder Theorem, Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Divisibility, Greatest Common Divisors and Bézout's Identity, Finite Counting, Factorials and Binomial Coefficients, Relations, Functions, and Quotients, The ZFC Axioms and the Basic Set Constructions
• Ideals and Quotient Rings: Examples and Counterexamples rests on Congruences, the Integers Modulo n and the Chinese Remainder Theorem, Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Divisibility, Greatest Common Divisors and Bézout's Identity, Finite Counting, Factorials and Binomial Coefficients, Foundations of the Real Numbers for Analysis, Order, Zorn's Lemma, and the Axiom of Choice, Primes, Euclid's Lemma and the Fundamental Theorem of Arithmetic, Relations, Functions, and Quotients, The ZFC Axioms and the Basic Set Constructions
• Ideals, Quotient Rings and the Isomorphism Theorems for Rings rests on Congruences, the Integers Modulo n and the Chinese Remainder Theorem, Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Divisibility, Greatest Common Divisors and Bézout's Identity, Finite Counting, Factorials and Binomial Coefficients, Foundations of the Real Numbers for Analysis, Order, Zorn's Lemma, and the Axiom of Choice, Relations, Functions, and Quotients, The ZFC Axioms and the Basic Set Constructions
• Modules, Submodules, Quotient Modules and the Isomorphism Theorems rests on Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Finite Counting, Factorials and Binomial Coefficients, Relations, Functions, and Quotients, The ZFC Axioms and the Basic Set Constructions
• Modules, Submodules, Quotient Modules and the Isomorphism Theorems: Examples and Counterexamples rests on Congruences, the Integers Modulo n and the Chinese Remainder Theorem, Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Divisibility, Greatest Common Divisors and Bézout's Identity, Relations, Functions, and Quotients, The ZFC Axioms and the Basic Set Constructions
• Monoids, Groups and Subgroups: Examples and Counterexamples rests on Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Foundations of the Real Numbers for Analysis, Relations, Functions, and Quotients, The ZFC Axioms and the Basic Set Constructions
• Normal Subgroups and Quotient Groups rests on Congruences, the Integers Modulo n and the Chinese Remainder Theorem, Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Divisibility, Greatest Common Divisors and Bézout's Identity, Finite Counting, Factorials and Binomial Coefficients, Foundations of the Real Numbers for Analysis, Relations, Functions, and Quotients, Roots, Rational Powers, and Classical Inequalities, The ZFC Axioms and the Basic Set Constructions
• Normal Subgroups and Quotient Groups: Examples and Counterexamples rests on Congruences, the Integers Modulo n and the Chinese Remainder Theorem, Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Divisibility, Greatest Common Divisors and Bézout's Identity, Finite Counting, Factorials and Binomial Coefficients, Foundations of the Real Numbers for Analysis, Relations, Functions, and Quotients, Roots, Rational Powers, and Classical Inequalities, The ZFC Axioms and the Basic Set Constructions
• Polynomial Rings and Roots: Examples and Counterexamples rests on Congruences, the Integers Modulo n and the Chinese Remainder Theorem, Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Divisibility, Greatest Common Divisors and Bézout's Identity, Finite Counting, Factorials and Binomial Coefficients, Foundations of the Real Numbers for Analysis, Primes, Euclid's Lemma and the Fundamental Theorem of Arithmetic, Relations, Functions, and Quotients, Roots, Rational Powers, and Classical Inequalities, The ZFC Axioms and the Basic Set Constructions
• Polynomial Rings, the Division Algorithm and Roots rests on Congruences, the Integers Modulo n and the Chinese Remainder Theorem, Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Divisibility, Greatest Common Divisors and Bézout's Identity, Finite Counting, Factorials and Binomial Coefficients, Foundations of the Real Numbers for Analysis, Order, Zorn's Lemma, and the Axiom of Choice, Primes, Euclid's Lemma and the Fundamental Theorem of Arithmetic, Relations, Functions, and Quotients, Roots, Rational Powers, and Classical Inequalities, The ZFC Axioms and the Basic Set Constructions
• Rings, Domains and Fields: Examples and Counterexamples rests on Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Divisibility, Greatest Common Divisors and Bézout's Identity, Finite Counting, Factorials and Binomial Coefficients, Foundations of the Real Numbers for Analysis, Relations, Functions, and Quotients, The ZFC Axioms and the Basic Set Constructions
• Rings, Subrings, Integral Domains and Fields rests on Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Divisibility, Greatest Common Divisors and Bézout's Identity, Finite Counting, Factorials and Binomial Coefficients, Foundations of the Real Numbers for Analysis, Relations, Functions, and Quotients, Roots, Rational Powers, and Classical Inequalities, The ZFC Axioms and the Basic Set Constructions
• Symmetric Groups and the Sign Homomorphism: Examples and Counterexamples rests on Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Divisibility, Greatest Common Divisors and Bézout's Identity, Finite Counting, Factorials and Binomial Coefficients, Foundations of the Real Numbers for Analysis, Relations, Functions, and Quotients, Roots, Rational Powers, and Classical Inequalities, The ZFC Axioms and the Basic Set Constructions
• Symmetric Groups, Cycle Decomposition and the Sign Homomorphism rests on Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Finite Counting, Factorials and Binomial Coefficients, Foundations of the Real Numbers for Analysis, Relations, Functions, and Quotients, Roots, Rational Powers, and Classical Inequalities, The ZFC Axioms and the Basic Set Constructions
• The Fundamental Theorem of Finite Abelian Groups rests on Congruences, the Integers Modulo n and the Chinese Remainder Theorem, Construction of the Natural Numbers, Construction of the Real Numbers via Cauchy Sequences, Countability and Uncountability, Divisibility, Greatest Common Divisors and Bézout's Identity, Finite Counting, Factorials and Binomial Coefficients, Foundations of the Real Numbers for Analysis, Primes, Euclid's Lemma and the Fundamental Theorem of Arithmetic, Relations, Functions, and Quotients, Roots, Rational Powers, and Classical Inequalities, The ZFC Axioms and the Basic Set Constructions