The Existence of K-Coefficient Fields in Commutative Algebras
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Authors
Haddix, George F.
Issue Date
1966
Volume
Issue
Type
Thesis
Language
en_US
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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.
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Publisher
Creighton University
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