Source: wikibot/unique-homomorphic-extension-theorem
= Unique homomorphic extension theorem
{wiki=Unique_homomorphic_extension_theorem}
The Unique Homomorphic Extension Theorem is a result in the field of algebra, particularly concerning rings and homomorphisms. It typically states that if you have a ring \\( R \\) and a subring \\( S \\), along with a homomorphism defined on \\( S \\), then there exists a unique (in the case of certain conditions) homomorphic extension of this mapping up to the whole ring \\( R \\).