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 共查询到18条相似文献,搜索用时 67 毫秒
1.
单纯Quantale及其Quantale商   总被引:8,自引:1,他引:7  
讨论Quantale上的同余与Quantale商之间的关系,研究单纯Quantale的性质,给出一类Quantale是单纯Quantale的等价刻画。最后从Quantale商的角度对单纯Quantale进行了研究,得到单纯Quantale的若干特征定理。  相似文献   

2.
给出模糊集Quantale的定义,在此基础上对Quantale与它对应的模糊集Quantale二者之间的关系进行比较,得到如果一个Quantale是可换的、单位的,则它的模糊集Quantale也是可换的、单位的结论。然后给出Quantale的一种嵌入方式。  相似文献   

3.
在对偶Quantale上定义了Par运算凵,并研究了其性质.给出了单位Quantale是对偶Quantale的充要条件,在此基础上得出对偶Quantale的等价刻画.证明了在一定条件下对偶Quantale的子Quantale亦是对偶Quantale.  相似文献   

4.
Quantale矩阵的广义逆及其正定性   总被引:2,自引:0,他引:2  
给出Quantale矩阵{1}-广义逆的一种刻划以及存在的条件,给出Quantale矩阵M-P广义逆的定义,讨论Quantale矩阵M-P广义逆的若干性质,得到Quantale矩阵M-P广义逆的具体形式.引入Quantale矩阵正定性的概念,研究交换幂等Quantale上矩阵正定的一些性质,得到交换幂等Quantale上矩阵正定的一些等价刻画.  相似文献   

5.
更好地讨论Quantale这一崭新数学分支的各种性质;给出幂等余Quantale及幂等左侧余Quantale的定义;幂等左侧余Quantale既是子余Quantale又是商余Quantale;且其补集是简单余Quantale;幂等余Quantale具有和其他Quantale类似的一些性质,并且与简单余Quantale也...  相似文献   

6.
讨论余Quantale的一些性质,引入预余Quantale的概念并给出预余Quantale成为余Quantale的充要条件,构造了一些子余Quantale结构。  相似文献   

7.
给出对合Quantale同余的概念,得到了对合Quantale同余的一些性质,讨论了对合Quantale同余与同态之间的关系,最后给出了对合Quantale乘积上的同余关系的结构。  相似文献   

8.
Quantale上的理想余核   总被引:2,自引:0,他引:2  
讨论Quantale理想与Quantale上映射之间的关系,同时给出Quantale上一个映射是理想余核的等价条件。  相似文献   

9.
夏常春  赵彬  韩胜伟 《数学学报》2018,61(5):811-822
本文给出了序半群上幂集Quantale的最大拓扑闭包的具体形式,即序半群的最小Quantale完备化.在此基础上,证明了Quantale范畴Quant是序半群范畴OSGrp*的满的反射子范畴.最后,给出了序半群Quantale完备化的一个应用.  相似文献   

10.
Quantale范畴的代数性   总被引:3,自引:2,他引:1  
刘智斌  赵彬 《数学学报》2006,49(6):1253-125
本文讨论了Quantale的范畴性质,给出了余等子和自由Quantale的结构,证明了Quantale范畴是代数范畴.  相似文献   

11.
引入了一类广义的L模糊Quantale,即(∈,∈∨q)-L模糊Quantale的定义,研究了其性质,利用它对经典子Quantale进行了等价刻画,证明了它的其中一种特殊情形就是L模糊Quantale。  相似文献   

12.
In this paper we prove that any quantale Q is (isomorphic to) a quantale of suitable relations on Q. As a consequence two isomorphism theorems are also shown with suitable sets of functions of Q into Q. These theorems are the mathematical background one needs in order to give natural and complete semantics for (non-commutative) Linear Logic using relations. Mathematics Subject Classification: 06D05, 06D10, 06D20, 03G25.  相似文献   

13.
The quantic conuclei on quantales   总被引:1,自引:0,他引:1  
In this paper, the main purpose is to investigate some properties of quantic conuclei. Firstly, the concept of an ideal conucleus is introduced and a characterization for a map to be an ideal conucleus is given. Secondly, the relations between quantic nuclei and quantic conuclei are studied on Girard quantale, based on which, the extensions of quantic conuclei (nuclei) to a Girard quantale and the relations between those extensions are discussed. Finally, the concrete structure of quantale without non-trivial quantic conuclei is given and it is proved that the number of subquantales of an infinite quantale is infinite.  相似文献   

14.
讨论理想Quantale的性质,给出了当Q是可换Quantale时,Q中理想都是半素理想的一个条件.引入了理想的扩张的概念,证明了与序半群中的一些经典结论相一致的命题.通过理想的扩张构造了一个Quantale上的同余,得到了当原理想是素理想时,这个同余所确定的Quantale商是Frame且找到了它的具体结构.  相似文献   

15.
在Quantale中引入了m系的概念,利用m系讨论了Quantale中素理想和半素理想之间的关系.在此基础上证明了当Q是可换Quantale时,Id(Q)是空间式Quantale当且仅当Q中的任一理想都是半素理想.最后把环和序半群中的素根定理推广到Quantak中,得到了Quantale中的素根定理.  相似文献   

16.
The central result of the paper claims that every integral quantale \(\mathbf {Q}\) has a natural embedding into the quantale of complete tolerances on the underlying lattice of \(\mathbf {Q}\). As an application, we show that the underlying lattice of any finite integral quantale is distributive in 1 and dually pseudocomplemented. Besides, we exhibit relationships between several earlier results. In particular, we give an alternative approach to Valentini’s ordered sets and show how the ordered sets are related to tolerances.  相似文献   

17.
The concept of quantale was created in 1984 to develop a framework for non-commutative spaces and quantum mechanics with a view toward non-commutative logic. The logic of quantales and its algebraic semantics manifests itself in a class of partially ordered algebras with a pair of implicational operations recently introduced as quantum B-algebras. Implicational algebras like pseudo-effect algebras, generalized BL- or MV-algebras, partially ordered groups, pseudo-BCK algebras, residuated posets, cone algebras, etc., are quantum B-algebras, and every quantum B-algebra can be recovered from its spectrum which is a quantale. By a two-fold application of the functor “spectrum”, it is shown that quantum B-algebras have a completion which is again a quantale. Every quantale Q is a quantum B-algebra, and its spectrum is a bigger quantale which repairs the deficiency of the inverse residuals of Q. The connected components of a quantum B-algebra are shown to be a group, a fact that applies to normal quantum B-algebras arising in algebraic number theory, as well as to pseudo-BCI algebras and quantum BL-algebras. The logic of quantum B-algebras is shown to be complete.  相似文献   

18.
序半群的Quantale完备化   总被引:2,自引:1,他引:1  
韩胜伟  赵彬 《数学学报》2008,51(6):1081-108
首先定义了集合上的闭包算子,研究了闭包算子的若干性质;其次给出了序半群的Quantale完备化,证明了序半群的Quantale完备化在同构意义下完全由序半群上的拓扑闭包决定;最后给出了序半群Quantale完备化的一个应用.  相似文献   

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