Algebra is one of the main branches of mathematics, covering the study of structure, relation and quantity. Algebra studies the effects of adding and multiplying numbers, variables, and polynomials, along with their factorization and determining their roots. In addition to working directly with numbers, algebra also covers symbols, variables, and set elements. Addition and multiplication are general operations, but their precise definitions lead to structures such as groups, rings, and fields.

Branches

Algebraic equations

An algebraic equation is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.

History

General algebra concepts

<!-- [Algebra[ ](https://bliptext.com/articles/talk-algebra-of-sets)of[ ](https://bliptext.com/articles/talk-algebra-of-sets)sets](https://bliptext.com/articles/algebra-of-sets)[ ](https://bliptext.com/articles/talk-algebra-of-sets)[ ](https://bliptext.com/articles/talk-algebra-of-sets)- [Algebraic[ ](https://bliptext.com/articles/talk-algebraic-normal-form)normal[ ](https://bliptext.com/articles/talk-algebraic-normal-form)form](https://bliptext.com/articles/algebraic-normal-form)[ ](https://bliptext.com/articles/talk-algebraic-normal-form)[ ](https://bliptext.com/articles/talk-algebraic-normal-form)- [Ampheck](https://bliptext.com/articles/ampheck)[ ](https://bliptext.com/articles/talk-ampheck)[ ](https://bliptext.com/articles/talk-ampheck)- [And-inverter graph](https://bliptext.com/articles/and-inverter-graph)[ ](https://bliptext.com/articles/talk-and-inverter-graph)[ ](https://bliptext.com/articles/talk-and-inverter-graph)- [Boole, George](https://bliptext.com/articles/george-boole)[ ](https://bliptext.com/articles/talk-george-boole)[ ](https://bliptext.com/articles/talk-george-boole)- [Boolean[ ](https://bliptext.com/articles/talk-boolean-algebra-structure)algebra[ ](https://bliptext.com/articles/talk-boolean-algebra-structure)(structure)](https://bliptext.com/articles/boolean-algebra-structure)[ ](https://bliptext.com/articles/talk-boolean-algebra-structure)[ ](https://bliptext.com/articles/talk-boolean-algebra-structure)- [Boolean[ ](https://bliptext.com/articles/talk-boolean-algebras-canonically-defined)algebras[ ](https://bliptext.com/articles/talk-boolean-algebras-canonically-defined)canonically[ ](https://bliptext.com/articles/talk-boolean-algebras-canonically-defined)defined](https://bliptext.com/articles/boolean-algebras-canonically-defined)[ ](https://bliptext.com/articles/talk-boolean-algebras-canonically-defined)[ ](https://bliptext.com/articles/talk-boolean-algebras-canonically-defined)- [Boolean conjunctive query](https://bliptext.com/articles/boolean-conjunctive-query) - [Boolean domain](https://bliptext.com/articles/boolean-domain)[ ](https://bliptext.com/articles/talk-boolean-domain)[ ](https://bliptext.com/articles/talk-boolean-domain)- [Boolean function](https://bliptext.com/articles/boolean-function)[ ](https://bliptext.com/articles/talk-boolean-function)[ ](https://bliptext.com/articles/talk-boolean-function)- [Boolean[ ](https://bliptext.com/articles/talk-boolean-algebra-logic)algebra[ ](https://bliptext.com/articles/talk-boolean-algebra-logic)(logic)](https://bliptext.com/articles/boolean-algebra-logic)[ ](https://bliptext.com/articles/talk-boolean-algebra-logic)[ ](https://bliptext.com/articles/talk-boolean-algebra-logic)- [Boolean implicant](https://bliptext.com/articles/implicant)[ ](https://bliptext.com/articles/talk-implicant)[ ](https://bliptext.com/articles/talk-implicant)- [Boolean[ ](https://bliptext.com/articles/talk-boolean-prime-ideal-theorem)prime[ ](https://bliptext.com/articles/talk-boolean-prime-ideal-theorem)ideal[ ](https://bliptext.com/articles/talk-boolean-prime-ideal-theorem)theorem](https://bliptext.com/articles/boolean-prime-ideal-theorem)[ ](https://bliptext.com/articles/talk-boolean-prime-ideal-theorem)[ ](https://bliptext.com/articles/talk-boolean-prime-ideal-theorem)- [Boolean-valued function](https://bliptext.com/articles/boolean-valued-function)[ ](https://bliptext.com/articles/talk-boolean-valued-function)[ ](https://bliptext.com/articles/talk-boolean-valued-function)- [Boolean-valued model](https://bliptext.com/articles/boolean-valued-model)[ ](https://bliptext.com/articles/talk-boolean-valued-model)[ ](https://bliptext.com/articles/talk-boolean-valued-model)- [Boolean[ ](https://bliptext.com/articles/talk-boolean-satisfiability-problem)satisfiability[ ](https://bliptext.com/articles/talk-boolean-satisfiability-problem)problem](https://bliptext.com/articles/boolean-satisfiability-problem)[ ](https://bliptext.com/articles/talk-boolean-satisfiability-problem)[ ](https://bliptext.com/articles/talk-boolean-satisfiability-problem)- [Boole's syllogistic](https://bliptext.com/articles/boole-s-syllogistic)[ ](https://bliptext.com/articles/talk-boole-s-syllogistic)[ ](https://bliptext.com/articles/talk-boole-s-syllogistic)- [Canonical[ ](https://bliptext.com/articles/talk-normal-form-boolean-algebra)form[ ](https://bliptext.com/articles/talk-normal-form-boolean-algebra)(Boolean[ ](https://bliptext.com/articles/talk-normal-form-boolean-algebra)algebra)](https://bliptext.com/articles/canonical-form-boolean-algebra)[ ](https://bliptext.com/articles/talk-normal-form-boolean-algebra)[ ](https://bliptext.com/articles/talk-normal-form-boolean-algebra)- [Characteristic function](https://bliptext.com/articles/characteristic-function)[ ](https://bliptext.com/articles/talk-characterisitic-function)[ ](https://bliptext.com/articles/talk-characterisitic-function)- [Compactness theorem](https://bliptext.com/articles/compactness-theorem)[ ](https://bliptext.com/articles/talk-compactness-theorem)[ ](https://bliptext.com/articles/talk-compactness-theorem)- [Complete[ ](https://bliptext.com/articles/talk-complete-boolean-algebra)Boolean[ ](https://bliptext.com/articles/talk-complete-boolean-algebra)algebra](https://bliptext.com/articles/complete-boolean-algebra)[ ](https://bliptext.com/articles/talk-complete-boolean-algebra)[ ](https://bliptext.com/articles/talk-complete-boolean-algebra)- [Consensus theorem](https://bliptext.com/articles/consensus-theorem)[ ](https://bliptext.com/articles/talk-consensus-theorem)[ ](https://bliptext.com/articles/talk-consensus-theorem)- [De[ ](https://bliptext.com/articles/talk-augustus-de-morgan)Morgan,[ ](https://bliptext.com/articles/talk-augustus-de-morgan)Augustus](https://bliptext.com/articles/augustus-de-morgan)[ ](https://bliptext.com/articles/talk-augustus-de-morgan)[ ](https://bliptext.com/articles/talk-augustus-de-morgan)- [De[ ](https://bliptext.com/articles/talk-de-morgan-s-laws)Morgan's[ ](https://bliptext.com/articles/talk-de-morgan-s-laws)laws](https://bliptext.com/articles/de-morgan-s-laws)[ ](https://bliptext.com/articles/talk-de-morgan-s-laws)[ ](https://bliptext.com/articles/talk-de-morgan-s-laws)- [Duality[ ](https://bliptext.com/articles/talk-duality-order-theory)(order[ ](https://bliptext.com/articles/talk-duality-order-theory)theory)](https://bliptext.com/articles/duality-order-theory)[ ](https://bliptext.com/articles/talk-duality-order-theory)[ ](https://bliptext.com/articles/talk-duality-order-theory)- [Entitative graph](https://bliptext.com/articles/entitative-graph)[ ](https://bliptext.com/articles/talk-entitative-graph)[ ](https://bliptext.com/articles/talk-entitative-graph)- [Espresso heuristic logic minimizer](https://bliptext.com/articles/minilog) - [Existential graph](https://bliptext.com/articles/existential-graph)[ ](https://bliptext.com/articles/talk-existential-graph)[ ](https://bliptext.com/articles/talk-existential-graph)- [First-order logic](https://bliptext.com/articles/first-order-logic)[ ](https://bliptext.com/articles/talk-first-order-logic)[ ](https://bliptext.com/articles/talk-first-order-logic)- [Formal system](https://bliptext.com/articles/formal-system)[ ](https://bliptext.com/articles/talk-formal-system)[ ](https://bliptext.com/articles/talk-formal-system)- [Free[ ](https://bliptext.com/articles/talk-free-boolean-algebra)Boolean[ ](https://bliptext.com/articles/talk-free-boolean-algebra)algebra](https://bliptext.com/articles/free-boolean-algebra)[ ](https://bliptext.com/articles/talk-free-boolean-algebra)[ ](https://bliptext.com/articles/talk-free-boolean-algebra)- [Heyting algebra](https://bliptext.com/articles/heyting-algebra)[ ](https://bliptext.com/articles/talk-heyting-algebra)[ ](https://bliptext.com/articles/talk-heyting-algebra)- [Indicator function](https://bliptext.com/articles/indicator-function)[ ](https://bliptext.com/articles/talk-indicator-function)[ ](https://bliptext.com/articles/talk-indicator-function)- [Interior algebra](https://bliptext.com/articles/interior-algebra)[ ](https://bliptext.com/articles/talk-interior-algebra)[ ](https://bliptext.com/articles/talk-interior-algebra)- [Jevons,[ ](https://bliptext.com/articles/talk-william-stanley-jevons)William[ ](https://bliptext.com/articles/talk-william-stanley-jevons)Stanley](https://bliptext.com/articles/william-stanley-jevons)[ ](https://bliptext.com/articles/talk-william-stanley-jevons)[ ](https://bliptext.com/articles/talk-william-stanley-jevons)- [Johnston diagram](https://bliptext.com/articles/johnston-diagram)[ ](https://bliptext.com/articles/talk-johnston-diagram)[ ](https://bliptext.com/articles/talk-johnston-diagram)- [Karnaugh map](https://bliptext.com/articles/karnaugh-map)[ ](https://bliptext.com/articles/talk-karnaugh-map)[ ](https://bliptext.com/articles/talk-karnaugh-map)- [Laws[ ](https://bliptext.com/articles/talk-laws-of-form)of[ ](https://bliptext.com/articles/talk-laws-of-form)Form](https://bliptext.com/articles/laws-of-form)[ ](https://bliptext.com/articles/talk-laws-of-form)[ ](https://bliptext.com/articles/talk-laws-of-form)- [Lindenbaum–Tarski algebra](https://bliptext.com/articles/lindenbaum-tarski-algebra)[ ](https://bliptext.com/articles/talk-lindenbaum-tarski-algebra)[ ](https://bliptext.com/articles/talk-lindenbaum-tarski-algebra)- [Logic gate](https://bliptext.com/articles/logic-gate)[ ](https://bliptext.com/articles/talk-logic-gate)[ ](https://bliptext.com/articles/talk-logic-gate)- [Logical connective](https://bliptext.com/articles/logical-connective)[ ](https://bliptext.com/articles/talk-logical-connective)[ ](https://bliptext.com/articles/talk-logical-connective)- [Logical graph](https://bliptext.com/articles/logical-graph)[ ](https://bliptext.com/articles/talk-logical-graph)[ ](https://bliptext.com/articles/talk-logical-graph)- [Logical matrix](https://bliptext.com/articles/logical-matrix)[ ](https://bliptext.com/articles/talk-logical-matrix)[ ](https://bliptext.com/articles/talk-logical-matrix)- [Logical value](https://bliptext.com/articles/logical-value)[ ](https://bliptext.com/articles/talk-logical-value)[ ](https://bliptext.com/articles/talk-logical-value)- [Minimal[ ](https://bliptext.com/articles/talk-minimal-negation-operator)negation[ ](https://bliptext.com/articles/talk-minimal-negation-operator)operator](https://bliptext.com/articles/minimal-negation-operator)[ ](https://bliptext.com/articles/talk-minimal-negation-operator)[ ](https://bliptext.com/articles/talk-minimal-negation-operator)- [Monadic[ ](https://bliptext.com/articles/talk-monadic-boolean-algebra)Boolean[ ](https://bliptext.com/articles/talk-monadic-boolean-algebra)algebra](https://bliptext.com/articles/monadic-boolean-algebra)[ ](https://bliptext.com/articles/talk-monadic-boolean-algebra)[ ](https://bliptext.com/articles/talk-monadic-boolean-algebra)- [Peirce,[ ](https://bliptext.com/articles/talk-charles-peirce)Charles[ ](https://bliptext.com/articles/talk-charles-peirce)Sanders](https://bliptext.com/articles/charles-peirce)[ ](https://bliptext.com/articles/talk-charles-peirce)[ ](https://bliptext.com/articles/talk-charles-peirce)- [Peirce's law](https://bliptext.com/articles/peirce-s-law)[ ](https://bliptext.com/articles/talk-peirce-s-law)[ ](https://bliptext.com/articles/talk-peirce-s-law)- [Propositional calculus](https://bliptext.com/articles/propositional-calculus)[ ](https://bliptext.com/articles/talk-propositional-calculus)[ ](https://bliptext.com/articles/talk-propositional-calculus)- [Sole[ ](https://bliptext.com/articles/talk-sole-sufficient-operator)sufficient[ ](https://bliptext.com/articles/talk-sole-sufficient-operator)operator](https://bliptext.com/articles/sole-sufficient-operator)[ ](https://bliptext.com/articles/talk-sole-sufficient-operator)[ ](https://bliptext.com/articles/talk-sole-sufficient-operator)- [Stone,[ ](https://bliptext.com/articles/talk-marshall-harvey-stone)Marshall[ ](https://bliptext.com/articles/talk-marshall-harvey-stone)Harvey](https://bliptext.com/articles/marshall-harvey-stone)[ ](https://bliptext.com/articles/talk-marshall-harvey-stone)[ ](https://bliptext.com/articles/talk-marshall-harvey-stone)- [Stone duality](https://bliptext.com/articles/stone-duality)[ ](https://bliptext.com/articles/talk-stone-duality)[ ](https://bliptext.com/articles/talk-stone-duality)- [Stone's[ ](https://bliptext.com/articles/talk-stone-s-representation-theorem-for-boolean-algebras)representation[ ](https://bliptext.com/articles/talk-stone-s-representation-theorem-for-boolean-algebras)theorem[ ](https://bliptext.com/articles/talk-stone-s-representation-theorem-for-boolean-algebras)for[ ](https://bliptext.com/articles/talk-stone-s-representation-theorem-for-boolean-algebras)Boolean[ ](https://bliptext.com/articles/talk-stone-s-representation-theorem-for-boolean-algebras)algebras](https://bliptext.com/articles/stone-s-representation-theorem-for-boolean-algebras)[ ](https://bliptext.com/articles/talk-stone-s-representation-theorem-for-boolean-algebras)[ ](https://bliptext.com/articles/talk-stone-s-representation-theorem-for-boolean-algebras)- [Stone space](https://bliptext.com/articles/stone-s-representation-theorem-for-boolean-algebras) - [Topological[ ](https://bliptext.com/articles/talk-topological-boolean-algebra)Boolean[ ](https://bliptext.com/articles/talk-topological-boolean-algebra)algebra](https://bliptext.com/articles/topological-boolean-algebra)[ ](https://bliptext.com/articles/talk-topological-boolean-algebra)[ ](https://bliptext.com/articles/talk-topological-boolean-algebra)- [Truth table](https://bliptext.com/articles/truth-table)[ ](https://bliptext.com/articles/talk-truth-table)[ ](https://bliptext.com/articles/talk-truth-table)- [Two-element[ ](https://bliptext.com/articles/talk-two-element-boolean-algebra)Boolean[ ](https://bliptext.com/articles/talk-two-element-boolean-algebra)algebra](https://bliptext.com/articles/two-element-boolean-algebra)[ ](https://bliptext.com/articles/talk-two-element-boolean-algebra)[ ](https://bliptext.com/articles/talk-two-element-boolean-algebra)- [Venn, John](https://bliptext.com/articles/john-venn)[ ](https://bliptext.com/articles/talk-john-venn)[ ](https://bliptext.com/articles/talk-john-venn)- [Venn diagram](https://bliptext.com/articles/venn-diagram)[ ](https://bliptext.com/articles/talk-venn-diagram)[ ](https://bliptext.com/articles/talk-venn-diagram)- [Zeroth-order logic](https://bliptext.com/articles/zeroth-order-logic) -->