模糊多属性决策在装备质量评价中的应用

从介绍装备质量的概念开始 ,揭示了装备质量评价的本质——模糊多属性决策 .建立了决策矩阵 ,采用层次分析法得到了各属性的权重 ,采用折衷型模糊多属性决策方法 ,在得到理想解与负理想解之后 ,计算了各方案与理想解和负理想解的欧几里得距离 ,并以远离负理想解为准则完成了装备方案的优选排序 .     

分区参数Gr\

对于含参数的多项式理想,提出了分区参数Gröbner基的概念,并且给出了一个计算分区参数Gröbner基的算法,证明了该算法的正确性和终止性.     

特征为2的素环的Lie理想上中心化自同构

Let R be a prime ring with an automorphism σ≠1, an identity map. Let L be a noncentral Lie ideal of R such that [x^σ,x] E Z for all x ∈ L, where Z is the center of R. Then L is contained in the center of R, unless char(R)=2 and dimc RC = 4.     

关于单状态变量的局部分岔问题中的内蕴理想

本文给出单状态变量的局部分岔问题中一类具有有限余维数的理想中最大内蕴理想的计算公式并且得到关于内蕴理想的两个充分必要条件.     

分次环的分次根

给出了建立分次环根的一般方法．作为其应用，建立了分次环的分次Brown—McCoy根，并给出了Brown—McCoy半单分次环的结构定理．     

On the notion of Cohen–Macaulayness for non-Noetherian rings

There exist many characterizations of Noetherian Cohen–Macaulay rings in the literature. These characterizations do not remain equivalent if we drop the Noetherian assumption. The aim of this paper is to provide some comparisons between some of these characterizations in non-Noetherian case. Toward solving a conjecture posed by Glaz, we give a generalization of the Hochster–Eagon result on Cohen–Macaulayness of invariant rings, in the context of non-Noetherian rings.     

Independence of vectors in codes over rings

We study codes over Frobenius rings. We describe Frobenius rings via an isomorphism to the product of local Frobenius rings and use this decomposition to describe an analog of linear independence. Special attention is given to codes over principal ideal rings and a basis for codes over principal ideal rings is defined. We prove that a basis exists for any code over a principal ideal ring and that any two basis have the same number of vectors. Hongwei Liu is supported by the National Natural Science Foundation of China (10571067).     

On Normed Lattices and Their Banach Completions

It is known that the Banach completion Y = bX of a normed lattice X need not preserve the properties to be Dedekind complete or σ-Dedekind complete. In this paper it is proved that the countable interpolation property and the property to be sequentially order complete are preserved under the Banach completion. To prove this results we found some sufficient conditions (which are close to necessary ones) on X which secure for Y to have the countable interpolation property and (respectively) to be sequentially order complete. These conditions are obtained with the help of the newly developed techniques based on representations of normed lattices. It is well known that order continuity, and σ-order continuity of a norm are preserved under the Banach completion. Here necessary and sufficient conditions on X to secure these properties in Y are discussed. Mathematics Subject Classification 2000: 46B42, 46E15     

A note on strong β-I-sets and strongly β-I-continuous functions

Summary In [6], we introduced and investigated the notions of strong β-I-open sets and strong β-I-continuous functions in ideal topological spaces. In this paper, we investigate further their important properties.     

Compact elements in the lattice of radicals

Summary A radical R, in the sense of Kurosh--Amitsur, is said to be compact if, given any collection of radicals X such that R ≤;VX, we have R ≤;VX' for some finite subcollection X' of X. A ring A is said to be radical compact if the lower radical on the singleton {A} is compact. This paper explores the relationship between radical compact rings and rings satisfying certain finiteness conditions. Closure properties of the class of all radical compact rings are also investigated.