广义Smooth格

作为由Weng所引入的smooth格和scott紧生成格的推广,引入了广义smooth 格和广义smooth代数格,讨论了它们的一些基本性质,证明了完备格L是广义完全分配格当且仅当L是广义smooth格和广义连续格.     

广义半Smooth格

引入了广义半Smooth格和广义半Smooth代数格的概念,讨论了它们的一些基本性质,证明了完备格L是广义完全分配格当且仅当L是拟连续的广义半Smooth格。     

群的正则带的KG-强半格分解

推广了著名的Petrich的完全正则半群为群的正规带当且仅当它为完全单半群的强半格的结果，证明了完全正则半群为群的正则(或右拟正规)带当且仅当它是完全单半群的HG(LG)-强半格．     

半连续格和半代数格的映射性质

研究了半连续格及半代数格的一些映射性质,讨论了强连续格的函数空间,给出了强连续格到方体的嵌入定理.     

正则带的拟强半格分解

本文研究了正则带的结构问题.利用拟强半格分解方法,获得了带为正则带当且仅当它为矩形带的拟强半格,推广了Yamada和Kimura关于正规带是矩形带的强半格的结果.     

基于格半群的有限状态自动机的同态

本文研究了格值有限状态自动机(LFSA)的同态和强同态及其性质.利用强同态概念,在格值有限状态自动机的状态集上建立了一种等价关系,得到了格值有限状态自动机的商自动机,证明了商自动机与强同态像自动机同构.     

交换半群的强半格

本文刻划交换半群的强半格上的最小半格同余，并证明由此得到的商半群为对应的每个交换半群的商半群的强半格。     

一类格序半群的同余

本文讨论了一类可换格序半群的同余性质。给出了这类格序半群同余的表示和同态分解定理。这个结论一般化了［１］和［２］中的结果。     

半连续格的半素极小集与序同态扩张

对完备格引入半素极小集的概念,证明完备格L为半连续格当且仅当L中的每个元在L中存在半素极小集,给出半连续格的两个序同态扩张定理.     

Strongly Pseudoalgebraic Lattices

In the recent twenty years,the generalizations of continuous lattices have attracted aconsiderable deal of attention (see [1 -6] ) .The so-called generalized continuous lat-tices(GCL) (see[2 ] ) is one of the most successful generalizations of continuous lat-tices.In 1 990 ,Venugopalan gave the definition of pseudoalgebraic lattice and provedthat a complete lattice is a compact totally order-disconnected(Preistley) space with re-spect to the Lawson topology if and only if it is a pseadoalgeb…     

smooth群的smooth同态

在smooth群的基础上通过模糊函数给出了smooth群的同态概念,并对它的一些性质进行了讨论,得到了许多漂亮的结果。     

Fuzzy Ideals and Fuzzy Distributive Lattices

Our main objective is to study properties of a fuzzy ideals(fuzzy dual ideals).A study of special types of fuzzy ideals(fuzzy dual ideals) is also furnished.Some properties of a fuzzy ideals(fuzzy dual ideals) are furnished.Properties of a fuzzy lattice homomorphism are discussed.Fuzzy ideal lattice of a fuzzy lattice is defined and discussed.Some results in fuzzy distributive lattice are proved.     

完全分配格上的格值Smooth点式拟一致结构

在完全分配格上定义L—smooth点式拟一致结构概念，并研究它与点式拟一致结构之间的关系以及与smooth拓扑之间的关系，给出分解定理、表现定理及构造条件。     

Large Sets of Lattices without Order Embeddings

Let I and μ be an infinite index set and a cardinal, respectively, such that |I| ≤ μ and, starting from ?₀, μ can be constructed in countably many steps by passing from a cardinal λ to 2^λ at successor ordinals and forming suprema at limit ordinals. We prove that there exists a system X = {L_i: i ∈ I} of complemented lattices of cardinalities less than |I| such that if i, j ∈ I and φ: L_i → L_j is an order embedding, then i = j and φ is the identity map of L_i. If |I| is countable, then, in addition, X consists of finite lattices of length 10. Stating the main result in other words, we prove that the category of (complemented) lattices with order embeddings has a discrete full subcategory with |I| many objects. Still in other words, the class of these lattices has large antichains (that is, antichains of size |I|) with respect to the quasiorder “embeddability.” As corollaries, we trivially obtain analogous statements for partially ordered sets and semilattices.     

TL—子环上的TL—子模的格

研究TL－子环上TL－子模形成的格及其子格的性质,给出这些格之间的同态与同构定理。     

强n-凝聚环

设R是一个环,n是一个正整数.右R-模M称为强n-内射的,如果从任一自由右R-模F的任一n-生成子模到M的同态都可扩张为F到M的同态;右R-模V称为强n-平坦的,如果对于任一自由右R-模F的任一n-生成子模T,自然映射VT→VF是单的;环R称为左强n-凝聚的,如果自由左R-模的n-生成子模是有限表现的;环R称为左n-半遗传的,如果R的每个n-生成左理想是投射的.本文研究了强n-内射模,强n-平坦摸及左强n-凝聚环.通过模的强n-内射性和强n-平坦性概念,作者还给出了强n-凝聚环和n-半遗传环的一些刻画.