Abstract
Let A be a commutative algebra with base field K <= A. Let N be a maximal ideal of A and g the natural K-homomorphism of A onto A/N. We say that A has a coefficient field F for N if there exist a field F<=A such that gF = A/N, g/F (g restricted to F) is one-one and the identities of F and A coincide. We are mainly interested in the case P>=K. | The purpose of this thesis is to analyze the existence of F by regarding A/N as a composite. When regarding A/N as a composite of two fields L and M, we use the notation A/N = [f0L,f1M] where f0, f1 are K-isomorphisms into A/N.