35 articles
Subdirect product
A subdirect product is a subalgebra of a direct product of algebras that projects onto every factor, so each factor is a homomorphic image; introduced by Garrett Birkhoff in 1944, it underlies his subdirect representation theorem.
Term algebra
A term algebra, also known as an absolutely free or anarchic algebra, is the algebra of formal terms built from operation symbols and variables, serving as the canonical free algebra.
Universal algebra
Universal algebra is the branch of mathematics that studies algebraic structures themselves, treating groups, rings, and lattices uniformly; Garrett Birkhoff founded the modern subject in 1935.
Universal property
A universal property, also called a universal mapping property, defines a mathematical object by unique morphisms from every object of its category rather than by internal construction.
Variety (universal algebra)
In universal algebra, a variety, also known as an equational class, is a class of algebras defined by identities; Birkhoff introduced the concept in 1935.