臺灣博碩士論文加值系統

在本文中我們證明了所有能表示成有限個(n 個)非交換子域聯集的環都是半單右阿丁環，並且與Z^k_2 同構，其中n=2^k-1 。

We characterize rings which is a union of finitely many, say n, proper subskew fields. We will show that such a kind of rings must be semisimple right Artinian and is isomorphic to Z^k_2, the kth cartesian power of the two element field Z_2, where n=2^k-1

Contents
Abstract ‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 1
1. Introduction
1.1 The Density Theorem ‧‧‧‧‧‧‧‧‧‧‧‧ 2
1.2 The Wedderbrun’s Theorem‧‧‧‧‧‧‧‧‧‧ 8
1.3 Main Problem‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧24
2. Main Results‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 26
Reference‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 32

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[5] T. S. Blyth, Module theory, an approach to linear algebra, N2, Clarendon Press, Oxford, 1990.