带有自同态的有界分配格-应用数学专业论文.docxVIP

三峡大学硕士学位论文 三 峡 大 学 硕 士 学 位 论 文 PAGE IV PAGE IV Abstract This paper mainly discusses bounded distributive lattice with an endomorphism k . Firstly, we give the definition of bounded distributive lattice with an endomorphism and the related properties. And on this basis we give the different conditions on endomorphism k , obtain two special bounded distributive lattice with an endomorphism, namely e3,1D algebras and symmetric extended pseudocomplemented distributive lattice. In the fourth part of the article, we discussion the principal congruence on e3,1D algebras.Firstly, the definition of e3,1D algebras is given, and we investigate the properties of the e3,1D algebras congruence relations. Then an equality depiction on the principal congruence relation of e3,1D algebras is obtained, according to this depiction, we research the complement of e3,1D algebras and present the sufficient and necessary condition that the principal congruence relation of e3,1D algebras is complementary. Finally we give an investigation on congruence extension property, and prove that e3,1D algebras satisfy the congruence extension property. In the fifth part of the article, we give the definition and initiate an investigation into the principal congruence of the symmetric extended pseudocomplemented distributive lattice, discuss the quality depiction on the principal congruence relation of the extended pseudocomplemented distributive lattice, then we investigate the kernel ideal and cokernel filter of the symmetric extended pseudocomplemented distributive lattice, depict the congruence generated by an ideal. A necessary and sufficient condition on an ideal being a kernel ideal is presented. Moreover, the link between kernel ideal and cokernel filter is displayed. Key words: e3 ,D1 algebras symmetric extended pseudocomplemented distributive lattice principal congruence kernel ideal complement congruence extension 目 录 引 言 1 HYPERLINK \l _bookmark0 1 绪论 2 1.1 格理论简介 2 1.2 问题提出的背景 3 1