distributive lattice 中文意思是什麼

Congruence ideals and congruence relations of pseudocomplemented distributive lattice

偽補分配格的同余理想與同余關系

Results some equivalent statements are obtained concerning a semiring becoming a distributive lattice

結果給出了該類半環成為分配格的幾個等價命題。

Aim in order to prove a semiring whose additive reduct is a semilattice and multiplicative reduct is a inverse semigroup to be a distributive lattice

摘要目的求證加法導出是半格、乘法導出是逆半群的半環成為分配格的充要條件。

Main results are following : theorem 1. 9 let 5 is a - pseudo - strong distributive lattice semiring, 0 is a congruence of the definition in lemma 1. 4

所得的主要結果如下：定理1 9設為偽強分配格半環，為引理1 4中所定義的s上的同余。

In this paper, we shall give the structure of solutions of eigen equation of a matrix over a distributive lattice and characterize convergence of powers of a matrix over a distributive lattice in terms of the eigen sets

給出分配格上矩陣的本徵方程的解的結構，利用本徵方程的解集給出了矩陣冪收斂的一個等價刻劃

We prove that m has property ( p ) if and only if ( 11 ) let m be as in ( 10 ) then m and every weakly closed subspace including m have proverty ( p ) if and only if for any t b ( h }, there exist x, y h. such that ( 12 ) let a be a completely distributive subspace lattice algebra acting on a hilbert space, then the rank one subalgebra of a is dense in a if and only if, the weak closures of the first and the second preannihilators of a in the space of all trace class operators are reflexive

一弱閉運算元空間，稱州具有性質（ p ） ，如果州中秩一運算元生成的子空間在期中a一弱稠密.我們證得:川具有性質（ p ） ，等價于州: = { t丁扭） : tx任[州上習， z任火} . （ ll ）設川如（ l0 ）所述，則川以及包含川的每個a一弱閉子空間都具有性質（ p ） ，當且僅當，對任意t任側喲，都存在x ， ，任火使得t一x y州

The primary studies in this paper are the following : ( 1 ) we define a generalized alexandroff topology on an l - fuzzy quasi ordered set which is a generalization of the alexandroff topology on an ordinary quasi ordered set, prove that the generalized alexandroff topology on an l - quasi ordered set ( x, e ) can be obtained by the join of a family of the alexandroff topologies on it, a topology on any topological space can be represented as a generalized alexandroff topology on some l - quasi ordered set, and the generalized alexandroff topologies on l - fuzzy quasi ordered sets are generalizations of the generalized alexandroff topologies on generalized ultrametric spaces which are defined by j. j. m. m. rutten etc. ( 2 ) by introducing the concepts of the join of l - fuzzy set on an l - fuzzy partial ordered set with respect to the l - fuzzy partial order and l - fuzzy directed set on an l - fuzzy quasi ordered set ( with respect to the l - fuzzy quasi order ), we define l - fuzzy directed - complete l - fuzzy partial ordered set ( or briefly, l - fuzzy dcpo or l - fuzzy domain ) and l - fuzzy scott continuous mapping, prove that they are respectively generalizations of ordinary dcpo and scott continuous mapping, when l is a completely distributive lattice with order - reversing involution, the category l - fdom of l - fuzzy domains and l - fuzzy scott continuous mappings is isomorphic to a special kind of the category of v - domains and scott continuous mappings, that is, the category l - dcqum of directed - complete l - quasi ultrametric spaces and scott continuous mappings, and when l is a completely distributive lattice in which 1 is a molecule, l - fuzzy domains and l - fuzzy scott continuous mappings are consistent to directed lim inf complete categories and lim inf co ntinuous mappings in [ 59 ]

本文主要工作是： （ 1 ）在l - fuzzy擬序集上定義廣義alexandroff拓撲，證明了它是通常擬序集上alexandroff拓撲的推廣，一個l - fuzzy擬序集（ x ， e ）上的廣義alexandroff拓撲可以由其上一族alexandroff拓撲取並得到，任意一個拓撲空間的拓撲都可以表示為某個l - fuzzy擬序集上的廣義alexandroff拓撲，以及l - fuzzy擬序集上的廣義alexandroff拓撲是j . j . m . m . rutten等定義的廣義超度量空間上廣義alexandroff拓撲的推廣。 （ 2 ）通過引入l - fuzzy偏序集上的l - fuzzy集關于l - fuzzy偏序的並以及l - fuzzy擬序集上（關于l - fuzzy擬序）的l - fuzzy定向集等概念，定義了l - fuzzy定向完備的l - fuzzy偏序集（簡稱l - fuzzydcpo ，又叫l - fuzzydomain ）和l - fuzzyscott連續映射，證明了它們分別是通常的dcpo和scott連續映射的推廣，當l是帶有逆序對合對應的完全分配格時，以l - fuzzydomain為對象， l - fuzzyscott連續映射為態射的范疇l - fdom同構於一類特殊的v - domain范疇，即以定向完備的l -值擬超度量空間為對象， scott連續映射為態射的范疇l - dcqum ，以及當l是1為分子的完全分配格時， l - fuzzydomain和l - fuzzyscott連續映射一致於k . wagner在[ 59 ]中定義的定向liminf完備的-范疇和liminf連續映射。

The representation theories of mp - filter which is created by an non - empty set of a implication algebra on a partial ordered set with condition ( c ) are obtained at first. and it ' s proved that the set which contains all mp - filters of a implication algebra x, denoted by mf ( x ) = { f x f is a filter of x }, is a distributive lattice and a complete lattice also in the view of the concept of mp - filter. then the fuzzy filter of a implication algebra is discussed, and the relations between mp - filter and fuzzy filter are obtained

藉助于mp -濾子的概念，得到了偏序集上具有條件（ c ）的蘊涵代數中由非空集合所生成mp濾子的表示定理，證明了由其上所有mp -濾子組成的集合mf （ x ）是一個完備的分配格；得到了蘊涵代數中fuzzy濾子與mp濾子的關系，給出了fuzzy濾子成為fuzzy素濾子的若干刻畫；並利用mp -濾子和fuzzy濾子，刻畫了一類偏序集上蘊涵代數的結構。

First, according to the definition of strong distributive lattice of semirings, we define the pseudo - strong distributive lattice semiring s and the pseudo - direct product, and we prove that the pseudo - direct product that we just define is a semiring, then we prove that s is the pseudo - sub direct product of d and s / 9

首先根據半環的強分配格的定義，定義了偽強分配格半環和一個斗格半環r與任一半環t的偽直積，證明了我們所定義的偽直積是一個半環，並且證明了s是d與s的偽次直積。

And we describe the join r v p of a ring congruence r and an arbitrary congruence p on s. similarly, we discribe all the divisible semiring congruences on a distributive semiring. at last, we give the least distributive lattice congruence on a commutative distributive semiring and an idempotent distributi ve semiring

在第三部分給出一個分配半環上的所有可除半環同余，並且在此半環的滿的、閉的、自共軛的理想子半環形成的集合與此半環上的可除半環同余的集合之間建立了一個一一的、保序映射。

On the prime ideal space of distributive lattice with bounds, a representation of lattice implication algebra was given. and with the help of the limit of set, the properties of this representation were discussed. finally, some of properties of any subset ' s limit of lattice implication algebra have been proved

具體作了以下三方面的工作： 1 、在有界分配格的素理想空間上給出了格蘊涵代數的一個表示，並藉助集合的無限運算系統地討論了表示的性質，得出了格蘊涵代數中任意子集無限運算的若干性質。