Concerning the Direct Product of Algebras
J. L. Dorroh · Annals of Mathematics · 1935
Introduction. A set of elements closed under two operations, addition and multiplication, is called an algebra provided that it is an abelian group under addition and provided that multiplication is associative and both-side distributive with respect to addition.' It is the purpose of this paper to give a definition of the direct product of algebras which does not presuppose a basis, but which gives the ordinary direct product in case the algebras involved possess bases,2 and to determine the conditions under which the direct product of two algebras exists.