文档介绍：R (+) M ??? R ./ I ??????????????????:?????:?????????:????????:????????: 2006 ???????????????????????????????,???????,?????????(??????,?????????)??????(??щ????????)????????.??????????,??????щ????????????,???????????????.?????????????? 20 ??????????????,??????????????.?????????????:??, ??????,??,?????????,?????????,?????????????,??????????.??,????????????????. ?Ч????????????????????,Ч????М???Ч??????.?????????????????Ч??????. ??????????????? idealization ?????????,???????????. ?Ч??????,????? idealization ????????.??????? idealization ???????????б[28] ??????. ?????????? amalgamated duplication of mutative ring along an ideal ?????????,???????????,?????????????. ?Ч??????????????? idealization ??????????.???, ?????????????????. ?????????:????,???,??,??. I The Zero-divisor Graphs of R (+) M and R ./ I Author: Zhongwei Wu Supervisor: Prof. Peimin Deng Subject: Mathematics Major: Algebra and its Applications Grade: 2006 Abstract The theory of mutative rings is a very active area which is not only of great theoretical interest in itself but also found important applications both within mathematics (for instance, binatorics, Finite Geometries and the Analysis Algorithms) and within the Engineering Sciences (in particular in Coding Theory and Sequence Design). especially ?in recent decades, there are more and more abundant research results of ?nite ring because of the ?nite ring play a more and more prominent role in coding areas. The study of algebraic structures, using properties of graphs, has e an exciting research topic in the last twenty years, leading to many fascinating results and questions. It lies at the crossroads of six areas: ring theory, group theory, semigroup theory, graph theory, elementary number theory binatorics. Like so many interdisciplinary studies, it has its fascinations, attractions, and also vast potential for future development. It has e an active research topic in recent years. In Chapter 1 of this paper, we summarize the history of the zero-divi