isomorphism theorems on algebraic systems
In this entry, all algebraic systems are of the same type; they are all -algebras. We list the generalizations of three famous isomorphism theorems, familiar to those who have studied abstract algebra in college.
If is a homomorphism from algebras and . Then
If is an algebra and are congruences on . Then
there is a unique homomorphism such that
where the downward pointing arrows are the natural projections of onto the quotient algebras (induced by the respective congruences).