The Existence of K-Coefficient Fields in Commutative Algebras

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.

Grantor dc:publisher

Creighton University

Year dc:date.issued

1966

Author dc:creator

• Haddix, George F.

Advisor dc:contributor.advisor

• Mordeson, John N.

Statement dc:rights

• A non-exclusive distribution right is granted to Creighton University and to ProQuest following the publishing model selected above.

Language dc:language.iso

en_US

Handle dc:identifier.uri

http://hdl.handle.net/10504/109970

OAI identifier oai:identifier

oai:cdr.creighton.edu:10504/109970