(∈,∈∨ q(λ,μ))-模糊强正则子半群

本文是正则半群的模糊化研究工作的继续,首先给出了广义模糊强正则子半群的概念,其次基于模糊点理论给出了(∈,∈∨ q(λ,μ))-模糊强正则子半群的概念,并且讨论了它们的相关性质.最后获得了(∈,∈∨ q(λ,μ))-模糊强正则子半群的同态像与同态原像的有关性质.     

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.     

幂格的同态与同余关系

本文在文[1]已引入幂格同态概念的基础上，进一步引入幂格同余关系的概念，并得到它们的一些相关性质．以及幂格同态与幂格同余关系的对应关系．     

(∈,∈∨q_(λ,μ))-模糊Γ-子环及同态

引入(∈,∈∨q(λ,μ))-模糊Γ-子环以及广义模糊Γ-子环的概念,给出它们的等价刻画,研究它们的交与并的性质。根据直积运算的定义,探讨广义模糊Γ-子环与(∈,∈∨q(λ,μ))-模糊Γ-环直积运算的性质。利用Γ-环满同态的定义,探讨(∈,∈∨q(λ,μ))-模糊Γ-子环的同态像及同态原像的相关性质,得到了(∈,∈∨q(λ,μ))-模糊Γ-子环的同态像及同态原像也是(∈,∈∨q(λ,μ))-模糊Γ-子环的结论。     

(λ,μ)直觉模糊子环(理想)

在直觉模糊集理论的基础上,首先引入了(λ,μ)直觉模糊子环和(λ,μ)直觉模糊理想的概念,讨论了它们的相关性质;其次在环同态的意义下,研究了(λ,μ)直觉模糊子环和(λ,μ)直觉模糊理想的同态像及其逆像.     

树自动机的同余与同态及其语言

从代数的角度出发研究树自动机的同余与同态,得出树自动机的同态基本定理和同构基本定理,进而研究它们之间语言的相关性质.     

FP-软布尔代数

将FP-软集(Fuzzy Parameterized Soft Sets)与布尔代数相结合,定义了FP-软布尔代数、FP-软布尔子代数、FP-软布尔代数的FP-软理想、FP-理想软布尔代数等概念,研究了它们的相关性质.最后,讨论了FP-软布尔代数的同态.     

L—Fuzzy群的同态与同构及其性质

本文在Ｌ－ｆｕｚｚｙ群的概念的基础上，用集合套概念定义了Ｌ－ｆｕｚｚｙ群间的同态与同构。进而给出了它们的一些性质。最后，我们给出了Ｌ－ｆｕｚｚｙ群的同态基本定理。     

乘积型模糊B-代数

引入乘积型模糊B-代数的概念,提供它们的几个例子,研究它们的一些性质.讨论模糊B-代数与乘积型模B-代数的关系,研究乘积型模糊B-代数的同态象与同态原象的性质,给出B-代数上乘积型模糊B-代数与B-代数的积代数上乘积型模糊B-代数的关系.     

de Bruijn-Good图的同态与自同构

本文研究了一般 de Bruijn-Good 图的同态,强同态,n 级强同态,(至少)n 级同态以及其自同构,对于不同级的 de Bruijn-Good 图,本文给出了它们各自同态集间的关系.     

Algebra homomorphisms defined via convoluted semigroups and cosine functions

Transform methods are used to establish algebra homomorphisms related to convoluted semigroups and convoluted cosine functions. Such families are now basic in the study of the abstract Cauchy problem. The framework they provide is flexible enough to encompass most of the concepts used up to now to treat Cauchy problems of the first- and second-order in general Banach spaces. Starting with the study of the classical Laplace convolution and a cosine convolution, along with associated dual transforms, natural algebra homomorphisms are introduced which capture the convoluted semigroup and cosine function properties. These correspond to extensions of the Cauchy functional equation for semigroups and the abstract d'Alembert equation for the case of cosine operator functions. The algebra homomorphisms obtained provide a way to prove Hille-Yosida type generation theorems for the operator families under consideration.     

On Homomorphisms of Fuzzy Groups

Clarification is suggested for the early notion of homomorphisms of fuzzy groups. Conditions are considered for fulfilment of various properties of homomorphisms of ordinary groups as well as properties specific to systems with a fuzzy operation. Correctness is discussed of the introduced notion of preservation of a fuzzy operation.     

On Homomorphisms of Fuzzy Groups

Clarification is suggested for the early notion of homomorphisms of fuzzy groups. Conditions are considered for fulfilment of various properties of homomorphisms of ordinary groups as well as properties specific to systems with a fuzzy operation. Correctness is discussed of the introduced notion of preservation of a fuzzy operation.     

Walkwise and admissible mappings between digraphs

We define two classes of mappings, between digraphs, which are closely related to homomorphisms and pathwise homomorphisms of finite automata. We show that the cycle rank cannot increase under mappings of these types, derive various decomposition properties, and then relate these mappings to homomorphisms of digraphs.     

Ring Homomorphisms and Finite Gorenstein Dimension

The local structure of homomorphisms of commutative noetherianrings is investigated from the point of view of dualizing complexes.A concept of finite Gorenstein dimension, which substantiallyweakens the notion of finite flat dimension, is introduced forhomomorphisms. It is shown to impose structural constraints,due to a remarkable equivalence of subcategories of the derivedcategory of all modules. An essential part of this study is the development of relativenotions of dualizing complexes and Bass numbers. It is provedthat the Bass numbers of local homomorphisms are rigid, extendinga known result for local rings. Quasi-Gorenstein homomorphismsare introduced as local homomorphisms that base-change a dualizingcomplex for the source ring into one for the target. They areshown to have the stability properties of the Gorenstein homomorphismthat they generalize. 1991 Mathematics Subject Classification:primary 13H10, 13D23, 14E40; secondary 13C15.     

Fuzzy HX环

引入Fuzzy HX环、正则Fuzzy HX环和一致Fuzzy HX环概念，讨论了它们结构和性质及其有关同态与同构关系。     

III-Homomorphisms and III-congruences on posets

A new homomorphism between two partially ordered sets (the III-homomorphism) and a new congruence on a poset (the III-congruence) are introduced. Some properties of these homomorphisms and congruences and their relationship to the other known homomorphisms and congruences on posets are investigated. In contrast to total algebras, there are many different ways to introduce these notions. It is usually required that the respective notions should coincide with the usual definitions whenever lattices or semilattices are treated. The present paper presents an approach which in some sense completes the hierarchy of definitions so far used.     

Completeness and an extension theorem for continuous fuzzy linear order-homomorphisms

In this paper, the notions of λ-Cauchy net and completeness in L-topological vector spaces are introduced, and some of their properties are studied. An extension theorem for continuous fuzzy linear order homomorphisms is proved.     

Green’s relations in some categories of strong graph homomorphisms

The immédiate purpose of this paper is to show how Li’s characterization of Green’s relations on monoids of strong endomorphisms of graphs [8] is related to earlier work of Klasa [5] on catégories. Li’s results are thus extended to some catégories of strong graph homomorphisms with more than one object, and a finiteness requirement is weakened. A further purpose is to extend Klasa’s results in such a way as to better reflect the factorization properties of interesting concrète catégories.     

Remarks on Priestley duality for distributive lattices

The notion of a Priestley relation between Priestley spaces is introduced, and it is shown that there is a duality between the category of bounded distributive lattices and 0-preserving join-homomorphisms and the category of Priestley spaces and Priestley relations. When restricted to the category of bounded distributive lattices and 0-1-preserving homomorphisms, this duality yields essentially Priestley duality, and when restricted to the subcategory of Boolean algebras and 0-preserving join-homomorphisms, it coincides with the Halmos-Wright duality. It is also established a duality between 0-1-sublattices of a bounded distributive lattice and certain preorder relations on its Priestley space, which are called lattice preorders. This duality is a natural generalization of the Boolean case, and is strongly related to one considered by M. E. Adams. Connections between both kinds of dualities are studied, obtaining dualities for closure operators and quantifiers. Some results on the existence of homomorphisms lying between meet and join homomorphisms are given in the Appendix.