文档介绍：西北大学硕士学位论文广义格及广义格上的微分姓名:李毅君申请学位级别:硕士专业:计算数学指导教师:辛小龙 20090612 广义格及广义格上的微分摘要代数系统上的微分结构的研究,为代数学的研究开辟了新的领域,提供了新的方法和思路,极大的扩展了代数学应用的范围。近年来由于序与偏序集理论在组合数学、Fuzzy数学、计算机科学、编码理论、甚至社会科学中得到了广泛的应用,因而使格论有了较大的发展。许多数学工作者从不同的方向将格的概念广义化,得到了一些广义格代数系统。自然的,广义格性质的研究也相应产生。基于利用格上的微分刻画格的性质,本文将微分的概念引入两类广义格,即A一格、 ,研究了相关性质,讨论了不同代数结构上微分性质的异同,将格微分的性质进行了推广。本文的内容主要分为四章。第一章介绍了格相关理论的研究历史和本文的选题背景及课题意义,简述了本文所取得的主要成果。第二章介绍了本文所需要的偏序集、格及格上微分的相关知识。,讨论了两种广义格微分的相关性质,将格微分的性质推广到了两种广义格上。关键词偏序集,格,广义格,微分 Abstract The research ofdifferential structure on thealgebrasystem,has opened up anew field fortheresearchofalgebra,and offered anew method and thinking,greatly expanded the scope ofapplication ofalgebra. In recent years,as order and partial ordered settheory were widely applied binatorics,puter science,and even inthe social science,the latticetheory hasbecame allimportantbranch algebra systems were obtained in various attempts togeneralize theconcept of theresearch of properties ofgeneral latticegenerated accordingly. Based on thestudy ofderivations on lattices,this paper introduced the concept of derivation on two kinds ofgeneralized lattice,named A—latticeandWA-lattice,thus the concept ofderivations on relativeproperties weregiven inthepaper,thesimilarities and differences of derivations between thetwokinds ofalgebra structure were alsodiscussed. This dissertationCanbedivided firstchapter isan introduction tothe history of emphasize that the thesis ismainly concemed、^,ithsome important general latticesarising puter second chapter,which serves asthebasis of our discussion,gives the otions and resultsofposets,lattices and derivations On the lasttwo chapters,we define the notions ofderivations on A—lattice andWA·lattice,and give some basicproperties ofthem. Key words Poset,Lattice,General Lattice,Derivation 西北大学学位论文知识产权声明书本人完全了解西北大学关于收集、保存、使用学位论文的规定。学校有