格的若干软代数结构
发布时间：2018-08-31 15:07
【摘要】：本文给出了反软子格、格的反软理想、格的新型软素理想、格的软同余的概念,并讨论它们的等价条件和一些相关的性质。取得的主要结果概括如下:在第三章中,先给出反软子格的概念以及两个反软子格分别在限制并和或的运算下仍然是反软子格。然后得到它的一些等价刻画。另外还研究了反软子格同态像、同态原像的性质。最后在全体反软子格组成的集合H上引入链条件并讨论H是阿丁的或诺特的充要条件。在第四章中,首先给出格的反软理想新概念。然后讨论两个反软理想分别在限制并、或运算下仍然是反软理想。最后在全体反软理想组成的集合H上引入链条件并讨论H是阿丁的或诺特的充要条件。在第五章中,将参数集赋予格的代数结构,给出格的新型软素理想的概念。然后利用扩张原理讨论格的新型软素理想的像与原像的性质。最后在全体新型软素理想组成的集合H上引入链条件,并获得H是阿丁的或诺特的充要条件。在第六章中,给出格上软同余的新定义。其次讨论了它的限制交和且的运算性质。最后讨论由同余θ及软同余F诱导的软同余在商格L/θ下仍是软同余的性质。
[Abstract]:In this paper, the concepts of anti-soft sublattices, anti-soft ideals of lattices, new soft prime ideals of lattices, soft congruences of lattices are given, and their equivalent conditions and some related properties are discussed. The main results obtained are summarized as follows: in Chapter 3, the concept of anti-soft sublattice and the two anti-soft sublattices are still anti-soft sublattices under the operation of restricted sum or respectively. Then some equivalent characterizations of it are obtained. In addition, the properties of the homomorphism image and homomorphic primitive image of anti-soft sublattice are studied. Finally, the chain condition is introduced on the set H of all anti-soft sublattices and the necessary and sufficient conditions for H to be Aden or Nott are discussed. In chapter 4, we first give a new concept of anti-soft ideal. Then it is discussed that two anti-soft ideals are still anti-soft ideals under restricted and or operation respectively. Finally, the chain condition is introduced on the set H of all anti-soft ideals and the necessary and sufficient conditions for H to be Aden or Nott are discussed. In chapter 5, the algebraic structure of lattice is given by parameter set, and the concept of new soft prime ideal is given. Then the properties of the image and the original image of the new soft prime ideal of lattice are discussed by using the extension principle. Finally, the chain condition is introduced on the set H of all new soft prime ideals, and the necessary and sufficient conditions for H to be Aden or Nott are obtained. In Chapter 6, a new definition of soft congruence is given. Secondly, the operation properties of the restricted intersection sum and its operation are discussed. Finally, the property that soft congruence induced by congruence 胃 and soft congruence F is still soft congruence under quotient lattice L / 胃 is discussed.
【学位授予单位】：江南大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O159
本文编号：2215359
[Abstract]:In this paper, the concepts of anti-soft sublattices, anti-soft ideals of lattices, new soft prime ideals of lattices, soft congruences of lattices are given, and their equivalent conditions and some related properties are discussed. The main results obtained are summarized as follows: in Chapter 3, the concept of anti-soft sublattice and the two anti-soft sublattices are still anti-soft sublattices under the operation of restricted sum or respectively. Then some equivalent characterizations of it are obtained. In addition, the properties of the homomorphism image and homomorphic primitive image of anti-soft sublattice are studied. Finally, the chain condition is introduced on the set H of all anti-soft sublattices and the necessary and sufficient conditions for H to be Aden or Nott are discussed. In chapter 4, we first give a new concept of anti-soft ideal. Then it is discussed that two anti-soft ideals are still anti-soft ideals under restricted and or operation respectively. Finally, the chain condition is introduced on the set H of all anti-soft ideals and the necessary and sufficient conditions for H to be Aden or Nott are discussed. In chapter 5, the algebraic structure of lattice is given by parameter set, and the concept of new soft prime ideal is given. Then the properties of the image and the original image of the new soft prime ideal of lattice are discussed by using the extension principle. Finally, the chain condition is introduced on the set H of all new soft prime ideals, and the necessary and sufficient conditions for H to be Aden or Nott are obtained. In Chapter 6, a new definition of soft congruence is given. Secondly, the operation properties of the restricted intersection sum and its operation are discussed. Finally, the property that soft congruence induced by congruence 胃 and soft congruence F is still soft congruence under quotient lattice L / 胃 is discussed.
【学位授予单位】：江南大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O159
【参考文献】
相关期刊论文 前10条
1 吴修竹;廖祖华;刘维龙;朱晓英;;反软子半群[J];模糊系统与数学;2015年05期
2 关贝贝;廖祖华;朱晓英;叶灵军;赵迪;叶婷;张士强;;软子半群[J];模糊系统与数学;2014年04期
3 叶灵军;廖祖华;朱晓英;赵迪;;软完全正则子半群[J];工程数学学报;2014年03期
4 郝翠芸;廖祖华;;(∈,∈∨q_((λ,μ)))-模糊正规子群的若干性质[J];数学杂志;2013年05期
5 罗晓棠;廖祖华;朱晓英;朱婵;刘晓妮;刘维龙;;半群的广义Ω-模糊双理想[J];江南大学学报(自然科学版);2013年04期
6 姜雪;廖祖华;刘春芝;张扬;曹姝;;(∈,∈∨_(q(λ,_)))-模糊强正则子半群[J];模糊系统与数学;2013年04期
7 刘春芝;廖祖华;姜雪;;(∈,∈∨_(q(λ,_)))-模糊布尔代数[J];模糊系统与数学;2013年04期
8 郝翠芸;廖祖华;嵇敏;潘玲;李云;王秋菊;;(■,■∨■(λ,μ))-模糊子群的若干性质[J];模糊系统与数学;2012年06期
9 张扬;廖祖华;曹姝;刘春芝;;(∈,∈∨q(λ,μ))-模糊正则子半群的同态性质[J];模糊系统与数学;2012年06期
10 殷霞;廖祖华;朱晓英;章里程;;软集与新型软子群[J];计算机工程与应用;2012年33期
，本文编号：2215359
本文链接：https://www.wllwen.com/shoufeilunwen/benkebiyelunwen/2215359.html
