L-Fuzzy子环的L-Fuzzy同态的刻画

给出L-fuzzy子环的L-fuzzy同态和L-fuzzy子环的L-fuzzy模的L-fuzzy同构的一种新刻画。     

L-Fuzzy子群与L-Fuzzy群同态

借助于L—fuzzy集的水平截集给出了L—fuzzy子群、L—fuzzy子环的一些新刻画．进一步给出了L-Fuzzy群同态与L—Fuzzy环同态的新刻画．     

L-Fuzzy子域与L-Fuzzy线性空间

本文在L是完全分配格时，给出L—Fuzzy子域和L—Fuzzy线性空间的定义，并以Lα-集合套和Lβ-集合套理论为基本工具给出它们的若干刻画．     

L-Fuzzy子格群的若干刻画

在L是完全分配格时，讨论L-Fuzzy子格群的一些特征性质。特别地，借助L—Fuzzy集的几种水平截集给出它的若干刻画。最后给出这些刻画的一个应用。     

L—Fuzzy集表现定理

简化文[1]引入的L－集合套概念的条件,并借助文[2]的结论给出L－Fuzzy表现定理的几种形式,进一步揭示普通集合簇与L－Fuzzy集之间的良好对应关系。     

L—Fuzzy集分解定理

随着隶属函数真值域的拓广,原来关于Zadch-Fuzzy集的分解定理II和III对于L－Fuzzy集不再成立,尽管已有一些它们的关于L＿Fuzzy集的改进形式,但因条件较强,失去了原来的许多优越性,本文从格论入手,首先引入格中元素的强上集和L－Fuzzy集准截集的两个新概念,并讨论了它们的部分性质,进而借助它们给出了L－Fuzzy集分解定理的两个新形式。     

格的L′—Fuzzy理想的代数性质

引入格L的L′－Fuzzy理想,L′－Fuzzy素理想和L′－Fuzzy同余理想等概念,讨论这些理想在Zadeh型映射下像的性质,得到若干结果。′′     

L-Fuzzy子群的L-Fuzzy直积

给出Luzzy子群的L-fuzzy直积的定义及等价刻画，并给出它的两个性质。     

L-Fuzzy子环的L-Fuzzy直和

研究了L-fuzzy集的水平截集的性质。然后给出了当L是完全分配格时L-fuzzy子环的L-fuzzy直和的定义，它是通常环的直和概念的推广，并借助于水平截集得到了关于它们的若干等价刻画。     

半环上Fuzzy k-理想的再定义

本文中，给出Fuzzy k－理想的新的概念作为半环上k－理想的新的模糊化概念，研究了半环同态下的Fuzzy k－理想的象及逆象的有关性质，并给出了非负整数半环N的Fuzzy k－理想的构造。     

L-fuzzy子环的L-fuzzy模的L-fuzzy同态

给出一种真正的 L- fuzzy子环的 L- fuzzy同态和 L- fuzzy同构等概念 ,证明 L- fuzzy模在 L- fuzzy同态映射下不变     

L-模糊集的L-模糊映射

引入L－模糊集的L－模糊映射,L－模糊单射,L－模糊满射及L－模糊双射等概念,并给出了它们的刻画。     

L—Fuzzy向量空间的同构

证明在双诱导映射及逆映射下L-Fuzzy向量空间的像和逆像仍是L-Fuzzy向量空间,给出L-Fuzzy向量空间同构的定义。     

On the endomorphism ring of a module with relative chain conditions

A well-known result of Small states that if M is a noetherian left R-module having endomorphism ring S then any nil subring of S is nilpotent. Fisher [4] dualized this result and showed that if M is left artinian then any nil ideal of S is nilpotent. He gave a bound on the indices of nilpotency of nil subrings of the endomorphism rings of noetherian modules and raised the dual question of whether there are such bounds in the case of artinian modules. He gave an affirmative answer if the module is also assumed to be finitely-generated. Similar affirmative answers for modules with finite homogeneous length were given in [10] and [15]. On the other hand, the nilpotence of certain ideals of the endomorphism rings of modules noetherian relative to a torsion theory has been extensively studied. See [2,6,8,12,15,17]. Jirasko [11] dualized, in some sense, some of the results of [6] to torsion modules satisfying the descending chain conditions with respect to some radical.

In this paper we give a bound of indices of nilpotency on nil subrings of the endomorphism ring of a left R-module which is T-torsionfree with respect to some torsion theory T on R-mod. As a special case, we obtain an affirmative answer to Fisher's question. We also note that our results can be stated in an arbitrary Grothendieck category.     

LF拓扑中满层性质的研究与应用

应用满层性质给出序列式空间的一个等价刻画,进而得到LF拓扑中的若干结论。     

L—Fuzzy拓扑空间的Os—连通性

在L－fuzzy拓扑空间中借助开集提出了一种具有fuzzy特色的Os-连通性,当s=0时,它就是O－连通性,讨论它的若干性质,证明它是L－好的推广。     

Coinduction for semigroup-graded rings

We describe the graded-simple modules over a semigroup-graded ring in terms of the simple modules over various component subrings. Our method utilizes the coinduction functors Coind_x .     

De Morgan Algebra of Metric Ⅲ

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L-fuzzy群理论的数理逻辑基础

Zadeh在文[1]中引入Fuzzy集概念之后，这一概念被Goguen[2]推广，真值域由单位闭区间被更一般的格所代替。Rosenfeld[3]将Zadeh的思想引入到群论中，提出Fuzzy群概念，真值域为格的Fuzzy群被称为L—fuzzy群[4]。本文的目的是用数理逻辑的语言陈述L—fuzzy群理论，构造L—fuzzy群的形式数学系统，从而建立L—fuzzy群理论的数理逻辑基础。     

On semilocal rings

We give several characterizations of semilocal rings and deduce that rationally closed subrings of semisimple artinian rings are semilocal, that artinian modules have semilocal endomorphism rings, and that artinian modules cancel from direct sums. Dedicated to the memory of Pere Menal