An algebraic construction is a method by which an algebraic entity is defined or derived from another. Instances include:
Cayley–Dickson construction Proj construction Grothendieck group Gelfand–Naimark–Segal construction Ultraproduct ADHM construction Burnside ring Simplicial set Fox derivative Mapping cone (homological algebra) Prym variety Todd class Adjunction (field theory) Vaughan Jones construction Strähle construction Coset construction Plus construction Algebraic K-theory Gelfand–Naimark–Segal construction Stanley–Reisner ring construction Quotient ring construction Ward's twistor construction Hilbert symbol Hilbert's arithmetic of ends Colombeau's construction Vector bundle Integral monoid ring construction Integral group ring construction Category of Eilenberg–Moore algebras Kleisli category Adjunction (field theory) Lindenbaum–Tarski algebra construction Freudenthal magic square Stone–Čech compactification