超格上的商结构理论

【作者】 李小光；

【导师】 辛小龙；

【作者基本信息】 西北大学 ， 计算数学， 2007， 硕士

【摘要】 超代数系统理论是非常重要的现代数学分支，许多专家学者对其进行了深入细致的系统研究。本文主要在超格上引入了加法(乘法)扩张、对换超格等概念，在此基础上构建出商超格，研究商超格的一些性质，更进一步地建立了第一、第二、第三同构定理。同时也对格蕴涵代数上的强LI-理想做了初步的讨论。第一章，我们对超格理论研究的背景、现状和格的基础知识作了简要的介绍。第二、三章，我们分别研究超格上的商代数和超格上的商结构，以及相关的一些性质。利用引入超格的乘法(加法)扩张，对换超格等概念，引出超格的陪集，构造出商超格。在此基础上，也进一步研究了商超格的对换性和商超格的其它性质。第四章，研究了格蕴涵代数的强LI-理想，并讨论了它的一些性质。更多还原

【Abstract】 The theory of hyperalgebra is a very important class of mathematics. Many experts and scholars thorough, painstakingly and systematically investigate it. In this paper we mainly introduce the concepts of multiplication (or addition) extension and transposition. The quotient hyperlattices is constructed, and some properties of quotient hyperlattices is also studied. Moreover the First, Second and Third Isomorphism Theorems have been established.In chapter 1, we simply introduce the background and the present state of the theory of the hyperlattice; for the sake of convenience, we introduce some fundamental knowledge about lattice. In chapter 2, 3 we study the quotient algebras of hyperlattice and the quotient structures of hyperlattice , and some properties of quotient hyperlattices. According to introducing the concepts of multiplication (or addition) extension and transposition, the cosets of hyperlattice is studied and the quotient hyperlattices is constructed. On the basis, we study the transposition of quotient hyperlattices and other properties of quotient hyperlattices. In chapter 4 we study the strong Li-ideals in lattice implication algebra. Some properties of the strong Li-ideals in lattice implication algebra is discussed.更多还原