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#### Existence of Coefficient Fields in Quasi-Local Rings

(Creighton University, 1965)

In the study of local algebra many results concerning coefficient fields in local rings have been discovered. The concept of a local ring was first introduced by Krull, who defined a local ring as a commutative ring R in ...

#### Eleven Conditions on Ideals in Commutative Rings

(Creighton University, 1966)

The purpose of this thesis is to compare eleven conditions which may be satisfied by ideals in commutative rings.

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

(Creighton University, 1966)

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 ...

#### The Convergence of a Non-Linear Parabolic Partial Differential Equation

(Creighton University, 1967)

This thesis is concerned with the application of Newton's method for multi-variable nonlinear functions to the nonlinear partial differential equation which describes two-dimensional flow of gas through porous media. | ...

#### The Existence of Coefficient Field Composites in Commutative Algebras

(Creighton University, 1967)

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 Boundary Value Problem in C2

(Creighton University, 1967)

Dirichlet's problem for a single complex variable may be stated thus: given a real valued function f which is continuous on the boundary of a region R, does there exist a function h such that it is harmonic on R, continuous ...

#### A Composite-Upper Bounding Method of Finding a Feasible Solution to a Linear Programming Problem

(Creighton University, 1967)

The purpose of this paper is to describe a synthesis of Wolfe's composite simplex algorithm1 and Dantzig's upper bounding technique2 to give a variation of the simplex method of obtaining a feasible solution to a linear ...

#### Coefficient Fields in Tensor Products

(Creighton University, 1967)

Let L>=K be fields of characteristic p /= 0 such that Lpe <= K for some positive integer e. Let M be an inbetween field of K and L and f the canonical K-homo-morphism of the tensor product L ⊗ M over K onto the field ...

#### Integration Over Converging Arcs in the Plane

(Creighton University, 1968)

Most standard theorems on convergence of integrals consider the integrals of a family of functions over a fixed domain of integration; however, situations occur in which one needs to approximate a curve over which a function ...

#### Applications of Coefficient Fields in Tensor Products

(Creighton University, 1968)

It will be the practice in this paper to use Barnes as the basis of terminology. Definitions not normally found in elementary algebra will be given. | As the title implies, the central theme of this paper is the study of ...