Some Properties of Partially Ordered Sets (open access)

Some Properties of Partially Ordered Sets

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
System: The UNT Digital Library
Direct Sums of Rings (open access)

Direct Sums of Rings

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.
System: The UNT Digital Library
Divisibility in Abelian Groups (open access)

Divisibility in Abelian Groups

This thesis describes properties of Abelian groups, and develops a study of the properties of divisibility in Abelian groups.
Date: August 1966
Creator: Huie, Douglas Lee
System: The UNT Digital Library
Semigroups (open access)

Semigroups

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.
System: The UNT Digital Library
On Bounded Variation (open access)

On Bounded Variation

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
System: The UNT Digital Library
Properties of Extended and Contracted Ideals (open access)

Properties of Extended and Contracted Ideals

This paper presents an introduction to the theory of ideals in a ring with emphasis on ideals in a commutative ring with identity.
Date: August 1966
Creator: Chan, George
System: The UNT Digital Library
The Role of the Quasigroup in the Development of Binary Systems (open access)

The Role of the Quasigroup in the Development of Binary Systems

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
System: The UNT Digital Library
A Fundamental Study of Cardinal and Ordinal Numbers (open access)

A Fundamental Study of Cardinal and Ordinal Numbers

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
System: The UNT Digital Library
Lattices (open access)

Lattices

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
System: The UNT Digital Library