Let be a class of algebraic systems (of the same type ). Consider an algebra generated by (http://planetmath.org/SubalgebraOfAnAlgebraicSystem) a set indexed by . is said to be a free algebra over , with free generating set , if for any algebra with any subset , there is a homomorphism such that .
If we define to be and to be , then freeness of means the existence of such that .
is free over itself (meaning consists of only) iff is free over some equational class.
If is an equational class, then free algebras exist in .
|Date of creation||2013-03-22 16:51:05|
|Last modified on||2013-03-22 16:51:05|
|Last modified by||CWoo (3771)|
|Synonym||free algebraic system|
|Defines||free generating set|