Subdirect product

In mathematics, especially in the areas of abstract algebra known as universal algebra, group theory, ring theory, and module theory, a subdirect product is a subalgebra of a direct product that depends fully on all its factors without however necessarily being the whole direct product. The notion was introduced by Birkhoff in 1944, generalizing Emmy Noether's special case of the idea (and decomposition result) for Noetherian rings, and has proved to be a powerful generalization of the notion of direct product.^{[citation needed]}