## The Existence of K-Coefficient Fields in Commutative Algebras

##### View/Open

##### Author

Haddix, George F.

Date

1966

Degree

MA (Master of Arts), Mathematics

1966

Degree

MA (Master of Arts), Mathematics

##### Metadata

Show full item record##### Abstract

Abstract

This thesis is concerned with the following problem. Let A be a commutative algebra over a subfield K of characteristic p /= 0. Let N be a maximal ideal of A and g the canonical homomorphism of A onto A/N. Denote A/N by F and identify K and gK. Assume F is pure inseparable over K. When does there exist a field in A, say F', such that gF = F and K <= F'? When the field F' above does exist it is called a K-coefficient field F' of A relative to N. The purpose of this thesis is to show that conditions appearing in (3), (4), and (5) for obtaining coefficient fields in commutative algebras and complete local rings are all equivalent to assumming that F has a subbasis over K (Definition 7.). This is done in Chapter I. In Chapter II it is shown that in the commutative algebra case the results of (3), (4), and (5) can be consolidated into a more general theorem by using the concept of subbasis. Then Chapter II is concluded with a theorem setting down conditions which insure the existence of a K-coefficient field in A which do not depend on the concept of subbasis.