This thesis investigates some of the properties of power series rings. The material is divided into three chapters. In Chapter I, some of the basic concepts of rings which are a prerequisite to an understanding of the definitions and theorems which follow are stated. Simple properties of power series rings are developed in Chapter II. Many properties of a ring R are preserved when we attach the indeterminant x to form the power series ring R[[x]]. Further results of power series rings are examined in Chapter III. An important result illustrated in this chapter is that power series rings possess some of the properties of rings of polynomials.

No description available.

My thesis deals with finding counterexamples to Lubin’s Conjecture. Lubin’s Conjecture states that for power series f, g with coefficients in Zp, and f invertible and non-torsion, g non-invertible, then if f ◦ g = g ◦ f , f , g are endomorphisms of a formal group over Zp. This conjecture connects formal power series over the ring of p-adic integers (Zp) to formal groups. In this paper I will explain the properties of Formal Groups, their endomorphisms and logarithms, and will illustrate some properties of power series over the rings Qp and Zp.

published_or_final_version / Mathematics / Master / Master of Philosophy

No description available.

Thesis (M. Phil.)--University of Hong Kong, 2000. / Includes bibliographical references (leaves 80-81).

Thesis (doctoral)--Friedrich-Wilhelms-Universität zu Berlin, 1908. / Vita.

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 (leaf: 54).

A study to deduce some fundamental properties of power series.

Thesis (Ph. D.)--University of Missouri-Columbia, 1998. / Typescript. Vita. Includes bibliographical references (leaf 93). Also available on the Internet.