r()m與r(215;)i的零因子圖

1、廣西師范大學(xué)碩士學(xué)位論文R（+）M與R（|×|）I的零因子圖姓名：吳中偉申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：鄧培民20090401The Zero-divisor Graphs of R(+)M and R ? ? IAuthor: Zhongwei Wu Supervisor: Prof. Peimin DengSubject: Mathematics Major: Algebra and its Applicatio

2、ns Grade: 2006AbstractThe theory of finite commutative rings is a very active area which is not only of great theoreticalinterest in itself but also found important applications both within mathematics (for instance,in C

3、ombinatorics, Finite Geometries and the Analysis Algorithms) and within the EngineeringSciences (in particular in Coding Theory and Sequence Design). especially，in recent decades,there are more and more abundant research

4、 results of finite ring because of the finite ring play amore and more prominent role in coding areas. The study of algebraic structures, using properties ofgraphs, has become an exciting research topic in the last twent

5、y years, leading to many fascinatingresults and questions. It lies at the crossroads of six areas: ring theory, group theory, semigrouptheory, graph theory, elementary number theory and combinatorics. Like so many interd

6、isciplinarystudies, it has its fascinations, attractions, and also vast potential for future development. It hasbecome an active research topic in recent years.In Chapter 1 of this paper, we summarize the history of the

7、zero-divisor graphs, and give thebackground and main results of this paper. At the same time, we give the notation and basicresults of ring theory and graph theory.In Chapter 2, we will determine the planarity of the zer

8、o-divisor graph of idealization of anycommutative ring and get some approving results. The main results of this chapter will be veryuseful in the following chapters.In Chapter 3, we will study the girth of the zero-divis

9、or graph of idealization, give more specificcharacterizations about the girth of the zero-divisor graph of idealization of any finite commutativerings than those given in [28].In Chapter 4, we will determine the planarit

10、y of the zero-divisor graph of amalgamated du-plication of a commutative ring along an ideal and get some satisfying results, and also study thediameter of the zero-divisor graph.In Chapter 5, we will discuss ideal-based