Thesis (Ph. D.)--University of Wisconsin--Madison, 1976. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaf 121).

The family of planar nearrings enjoys quite a few geometric and combinatoric properties. Circular planar nearrings are members of this family which have the character of circles of the complex plane. On the other hand, they also have some properties which one may not find among the circles of the complex plane. In this dissertation, we first review the definition and characterization of a planar nearring, and some various ways of constructing planar nearrings, as well as various ways of constructing BIBD's from a planar nearring. Circularity of a planar nearring is then introduced, and examples of circularity planar nearrings are given. Then, some nonisomorphic BIBD's arising from the same additive group of a planar nearring are examined. To provide examples of nonabelian planar nearrings, the structures of Frobenius groups with kernel of order 64 are completely determined and described. On the other hand, examples of Ferrero pairs (N, Φ)'s with nonabelian Φ, which produce circular planar nearrings, are provided. Finally, we study the structures of circular planar nearrings generated from the finite prime fields from geometric and combinatoric points of view. This study is then carried back to the complex plane. In turn, it gives a good reason for calling a block from a circular planar nearring a "circle."

The primary objective of this work is to discuss some of the elementary properties of near-rings as they are related to rings. This study is divided into three subdivisions: (1) Basic Properties and Concepts of Near-Rings; (2) The Ideal Structure of Near-Rings; and (3) Homomorphism and Isomorphism of Near-Rings.

Lok Tsan Ming. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (p. 82-83). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstract in Chinese.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1955. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1984. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 75-76).

We say that a commutative ring R has the unique decomposition into ideals (UDI) property if, for any R-module which decomposes into a _nite direct sum of indecomposable ideals, this decomposition is unique up to the order and isomorphism class of the ideals. In a 2001 paper, Goeters and Olberding characterize the UDI property for Noetherian integral domains and in a 2011 paper Ay and Klingler obtain similar results for Noetherian reduced rings. We characterize the UDI property for Noetherian rings in general. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2019. / FAU Electronic Theses and Dissertations Collection

Every ring has both left and right modules. In the theory of nearrings, only right modules are usually considered for left nearrings. The purpose of this report is to promote the study of an alternative type of nearring module. For left nearrings, these unusual modules are left modules. There are three reasons for studying left modules for left nearrings. These unusual nearring modules add an element of symmetry to the theory of nearrings. At the same time, comparing left and right modules of a left nearring illustrates how the theory of nearrings is distinct from ring theory. Finally, with two types of nearring modules, it is possible to carry over to nearring theory more concepts from ring theory; for example, duals of modules and bimodules. This report is an attempt to show that these reasons are valid. The first chapter is devoted to producing a well-reasoned definition for the unusual type of nearring module. It begins with a careful presentation of background material on nearrings, rings, and ring modules. This material is used to motivate the definitions for nearring modules, which are introduced in the third section. The second chapter is concerned with showing that the unusual type of nearring module can fit into the theory of nearrings. In the first section, several papers relevant to the study of these modules are summarized. The work of A. Frohlich on free additions is of primary importance. General construction methods for both types of nearring modules are then described. Finally, some general properties of left modules of left nearrings are examined. Examples of left modules for left nearrings are presented in the third chapter. First, the general constructions of the second chapter are applied in some particular cases. This leads naturally to structures that are analogous to bimodules and structures analogous to dual modules for ring modules. Here, free additions have a special role. Several dual nearring modules are examined in detail. The information needed to construct many more examples of nearring modules of the unusual type is also presented. Only small cyclic groups are used for these examples.

by Lam Che Pang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1994. / Includes bibliographical references (leaves 85-87). / Chapter 1 --- Preliminaries --- p.2 / Chapter 1.1 --- Introduction --- p.2 / Chapter 1.2 --- Ideals of Γ-nearrings --- p.6 / Chapter 1.3 --- Pierce-decomposition theorem --- p.14 / Chapter 1.4 --- Left SΓ and Right RΓ-bimodules --- p.19 / Chapter 2 --- D.G. Γ-nearrings and its modules --- p.25 / Chapter 2.1 --- Distributively generated Γ-nearrings --- p.25 / Chapter 3 --- Near-rings and Automata --- p.40 / Chapter 3.1 --- Monoids of semiautomaton and automaton --- p.40 / Chapter 4 --- Derivation in Γ-nearrings --- p.66 / Chapter 4.1 --- Derivation in Γ-nearrings --- p.66 / Chapter 4.2 --- Abelian conditions --- p.70 / Chapter 4.3 --- Unitary Γ-nearrings --- p.76 / Chapter 4.4 --- Decomposition of right Rr-modules --- p.81

Shan Chin-Chi. / Thesis (M.Phil.)--Chinese University of Hong Kong. / Bibliography: leaves 44-45.