UNT Libraries - 18 Matching Results

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Direct Sums of Rings

Description: This paper consists of a study of the direct sum U of two rings S and T. Such a direct sum is defined as the set of all ordered pairs (s1, t1), where s1 is an arbitrary element in S and t1 is an arbitrary element in T.
Date: August 1966
Creator: Hughes, Dolin F.
Item Type: Refine your search to only Thesis or Dissertation
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A Fundamental Study of Cardinal and Ordinal Numbers

Description: The purpose of this paper is to present a discussion on the basic fundamentals of the theory of sets. Primarily, the discussion will be confined to the study of cardinal and ordinal numbers. The concepts of sets, classes of sets, and families of sets will be undefined quantities, and the concept of the class of all sets will be avoided.
Date: August 1966
Creator: Thornton, Robert Leslie
Item Type: Refine your search to only Thesis or Dissertation
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Lattices

Description: Because lattice theory is so vast, the primary purpose of this paper will be to present some of the general properties of lattices, exhibit examples of lattices, and discuss the properties of distributive and modular lattices.
Date: August 1966
Creator: Rintala, Richard Arne
Item Type: Refine your search to only Thesis or Dissertation
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On Bounded Variation

Description: This paper is primarily concerned with developing the theory of real-valued functions of bounded variation and those ideas which are closely related to this main topic. In addition to this, some emphasis has been placed on the relationship of the theory of functions of bounded variation to specific areas of analysis. In particular, integration theory has been chosen as the vehicle to demonstrate this connection.
Date: August 1966
Creator: Lewis, Paul Weldon
Item Type: Refine your search to only Thesis or Dissertation
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The Role of the Quasigroup in the Development of Binary Systems

Description: The objective here is to give a logical development of some mathematical systems beginning with those having relatively little algebraic structure, and progressing to systems rich in structure. The discussion will commence with a mathematical system called the groupoid, a nonempty set with a binary operation.
Date: August 1966
Creator: Stingel, Charles Willard
Item Type: Refine your search to only Thesis or Dissertation
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Semigroups

Description: The purpose of this paper is to present some fundamental properties of algebraic semigroups. The development of the theory of semigroups has appeared for the most part in the past few years of this century. A semigroup is the result of a weakening of the axioms for a group. Thus all groups are semigroups. That the study of semigroups is very closely related to the abstract study of general transformations is, perhaps, one of the reasons for the rapid development of semigroup theory.
Date: August 1966
Creator: Jeter, Melvyn W.
Item Type: Refine your search to only Thesis or Dissertation
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Some Properties of Partially Ordered Sets

Description: It may be said of certain pairs of elements of a set that one element precedes the other. If the collection of all such pairs of elements in a given set exhibits certain properties, the set and the collection of pairs is said to constitute a partially ordered set. The purpose of this paper is to explore some of the properties of partially ordered sets.
Date: August 1966
Creator: Hudson, Philip Wayne
Item Type: Refine your search to only Thesis or Dissertation
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Topological Properties of Chains

Description: The purpose of this paper is to define and investigate some of the properties of chains. Particular attention is given to a natural topology for chains, called the interval topology, and how the chain properties and topological properties of chains affect each other.
Date: January 1966
Creator: Womack, Robert A.
Item Type: Refine your search to only Thesis or Dissertation
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Which Came First : The Measure or the Integral?

Description: This thesis provides a development of integration from two different points of view. In Chapter I, a measure and a measurable function are defined. A theory of integration is then developed in Chapter II based on the measure. In Chapter III, the integral is introduced directly without first going through the process of defining a measure, and a measure is developed from the integral. The concluding chapter shows the equivalence of the two integrals under rather general conditions.
Date: June 1966
Creator: Chapman, John Barnes
Item Type: Refine your search to only Thesis or Dissertation
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