abstract algebra

Affine Varieties

Handbook guide to Affine Varieties, covering core definitions, key results, formulas, reasoning methods and worked examples in graduate abstract algebra.

Affine Varieties and Finite Generation

Handbook guide to affine varieties and finite generation with core definitions, structural results, reasoning methods and verification checks.

Engineering Mathematics14 Aug 2026 · 10 min read

Affine Varieties and Polynomial Zero Sets

Handbook guide to affine varieties and polynomial zero sets, covering definitions, key results, methods, verification checks and worked examples.

Algebraic Closures

Handbook guide to Algebraic Closures, covering core definitions, key results, formulas, reasoning methods and worked examples in graduate abstract algebra.

Applications of Sylow Theory

Handbook guide to Applications of Sylow Theory, with key definitions, results, formulas, reasoning methods and worked examples for abstract algebra.

Arithmetic in Dedekind Domains

Handbook guide to Arithmetic in Dedekind Domains, with key definitions, results, formulas, reasoning methods and worked examples for abstract algebra.

Base Change in Tensor Products

Handbook guide to Base Change in Tensor Products, with key definitions, results, formulas, reasoning methods and worked examples for abstract algebra.

Engineering Mathematics14 Aug 2026 · 13 min read

Bilinear Forms and Orthogonality

Handbook guide to bilinear forms and orthogonality, covering definitions, key results, methods, verification checks and worked examples.

Engineering Mathematics14 Aug 2026 · 10 min read

Categories, Products, Coproducts and Functors

Handbook guide to categories, products, coproducts and functors with core definitions, structural results, reasoning methods and verification checks.

Engineering Mathematics14 Aug 2026 · 13 min read

Categories, Universal Constructions and Diagrams

Handbook guide to categories, universal constructions and diagrams, covering definitions, key results, methods, verification checks and worked examples.

Chain Complexes

Handbook guide to Chain Complexes, covering core definitions, key results, formulas, reasoning methods and worked examples in graduate abstract algebra.

Chain Complexes, Chain Maps and the Snake Lemma

Handbook guide to chain complexes, chain maps and the snake lemma with core definitions, structural results, reasoning methods and verification checks.

Chain Conditions and the Generator Lemma

Handbook guide to Chain Conditions and the Generator Lemma, with key definitions, results, formulas, reasoning methods and worked examples for abstract algebra.

Choice Principles and Maximality Methods

Handbook guide to choice principles and maximality methods, covering definitions, key results, methods, verification checks and worked examples.

Engineering Mathematics14 Aug 2026 · 13 min read

Commutative Rings, Domains, Units and Subrings

Handbook guide to commutative rings, domains, units and subrings, covering definitions, key results, methods, verification checks and worked examples.

Complex Numbers, Roots of Unity and Cyclotomic Polynomials

Handbook guide to complex numbers, roots of unity, with definitions, key results, methods, verification checks and worked examples.

Composition Series

Handbook guide to Composition Series, covering core definitions, key results, formulas, reasoning methods and worked examples in graduate abstract algebra.

Engineering Mathematics14 Aug 2026 · 9 min read

Composition Series, Solvable Groups and Nilpotent Groups

Composition Series, Solvable Groups and Nilpotent Groups: core definitions, structural results and verification methods in abstract algebra.

Computing Ext, Tor and Base Change

Handbook guide to computing ext, tor and base change with core definitions, structural results, reasoning methods and verification checks.

Computing Galois Groups and Finite Fields

Handbook guide to computing galois groups and finite fields with core definitions, structural results, reasoning methods and verification checks.

Computing Galois Groups Directly

Handbook guide to Computing Galois Groups Directly, with key definitions, results, formulas, reasoning methods and worked examples for abstract algebra.

Cosets, Normal Subgroups and Homomorphisms

Handbook guide to Cosets, Normal Subgroups and Homomorphisms, with key definitions, results, formulas, reasoning methods and worked examples for abstract algebra.

Engineering Mathematics14 Aug 2026 · 9 min read

Cosets, Normal Subgroups, Quotient Groups and Homomorphisms

Cosets, Normal Subgroups, Quotient Groups and Homomorphisms: core definitions, structural results and verification methods in abstract algebra.

Engineering Mathematics14 Aug 2026 · 12 min read

Cosets, Subgroup Index and Finite-Group Divisibility

Handbook guide to cosets, subgroup index and finite-group divisibility, covering definitions, key results, methods, verification checks and worked examples.

Crossed Product Algebras and Spectral Sequences

Handbook guide to crossed product algebras and spectral sequences, covering definitions, key results, methods, verification checks and worked examples.

Cyclic and Kummer Extensions

Handbook guide to Cyclic and Kummer Extensions, with key definitions, results, formulas, reasoning methods and worked examples for abstract algebra.

Cyclic Extensions, Kummer Extensions and Solvability by Radicals

Cyclic Extensions, Kummer Extensions and Solvability by Radicals: core definitions, structural results and verification methods in abstract algebra.

Cyclotomic Fields

Handbook guide to Cyclotomic Fields, covering core definitions, key results, formulas, reasoning methods and worked examples in graduate abstract algebra.

Cyclotomic Fields and Cubic Galois Groups

Handbook guide to cyclotomic fields and cubic galois groups with core definitions, structural results, reasoning methods and verification checks.

Dedekind Domains: Ideal Factorisation and Arithmetic

Handbook guide to dedekind domains: ideal factorisation and arithmetic with core definitions, structural results, reasoning methods and verification checks.

Derived Functors

Handbook guide to Derived Functors, covering core definitions, key results, formulas, reasoning methods and worked examples in graduate abstract algebra.

Derived Functors, Tor and Ext

Handbook guide to derived functors, tor and ext with core definitions, structural results, reasoning methods and verification checks.

Engineering Mathematics14 Aug 2026 · 14 min read

Determinants, Differential Forms and Bracket Algebras

Handbook guide to determinants, differential forms and bracket algebras, covering definitions, key results, methods, verification checks and worked examples.

Direct and Inverse Limits

Handbook guide to Direct and Inverse Limits, with key definitions, results, formulas, reasoning methods and worked examples for abstract algebra.

Engineering Mathematics14 Aug 2026 · 5 min read

Direct Products of Groups

Handbook guide to direct products of groups with core definitions, structural results, reasoning methods and verification checks.

Direct Sums and Free Modules

Handbook guide to Direct Sums and Free Modules, with key definitions, results, formulas, reasoning methods and worked examples for abstract algebra.

Direct Sums, Free Modules and Matrix Representations

Handbook guide to direct sums, free modules and matrix representations with core definitions, structural results, reasoning methods and verification checks.

Discriminants in Number Fields

Handbook guide to Discriminants in Number Fields, with key definitions, results, formulas, reasoning methods and worked examples for abstract algebra.

Divisible Abelian Groups

Handbook guide to Divisible Abelian Groups, with key definitions, results, formulas, reasoning methods and worked examples for abstract algebra.

Engineering Mathematics14 Aug 2026 · 10 min read

Division Algebras and Central Simple Algebras

Handbook guide to division algebras and central simple algebras, covering definitions, key results, methods, verification checks and worked examples.

Division-Norm Rings and Principal Ideal Methods

Handbook guide to division-norm rings and principal ideal methods, covering definitions, key results, methods, verification checks and worked examples.

Elementary Number Theory

Handbook guide to Elementary Number Theory, with key definitions, results, formulas, reasoning methods and worked examples for abstract algebra.

Embedding into an Injective Module

Handbook guide to Embedding into an Injective Module, with key definitions, results, formulas, reasoning methods and worked examples for abstract algebra.

Exact Functors

Handbook guide to Exact Functors, covering core definitions, key results, formulas, reasoning methods and worked examples in graduate abstract algebra.

Exact Functors and Projective Modules

Handbook guide to exact functors and projective modules with core definitions, structural results, reasoning methods and verification checks.