关于BCK-代数的模糊理想和超积

通过使用超滤子的概念以及所讨论的模糊理想的相应性质,提出了超积BCK-代数和BCK-代数模糊子集的模糊超积.     

BL-代数的模糊素理想

在BL-代数上,将模糊集理论应用到素理想理论中,引入了模糊素理想的概念,研究了模糊素理想的性质,获得了模糊素理想的若干刻画方法和模糊素理想延拓定理等重要结果,证明了由模糊素理想构造的模糊商BL-代数是一个MV-链.     

超BCK-代数的模糊超子代数

模糊超子代数的概念被引入并且一些相关性质被研究,模糊超BCK理想和模糊超子代数的关系被介绍,模糊超子代数的特征被陈述。     

BCH-代数的模糊理想与模糊H-理想

在BCK／BCI／BCC代数中Fuzzy理想被广泛研究，但在BCH-代数中还没有讨论过。在BCH-代数中引人了Fuzzy理想与FuzzyH-理想的概念，并讨论它们的性质。     

MV-代数的素滤子MV-拓扑空间

在MV-方体[0,1]X的子集Ω上引进MV-拓扑结构,并套论MV-拓扑空间的紧性、Hausdorff分离性等拓扑性质.细致地讨论MV-代数的素滤子集上的MV-拓扑空间(M,ΩM),证明素滤子MV-拓扑空间是紧Hausdorff MV-空间,并且它还是良紧空间.作为应用,证明一个σ-完备格M是MV-代数当且仅当M同构于某个Stone MV-空间的MV-开闭集格.     

BCI代数的闭Ω犹豫模糊理想

在集合Ω中,把犹豫模糊集、Ω模糊集相结合来研究BCI-代数.首先在BCI代数中引入闭Ω犹豫模糊理想的概念,讨论它的一些性质和等价刻画;其次,在闭犹豫模糊理想概念的基础上研究了如何构造闭Ω犹豫模糊理想,讨论了闭Ω犹豫模糊理想的同态像与同态原像的性质;最后,给出了闭Ω犹豫模糊理想与乘积型BCI代数的闭Ω犹豫模糊理想的关系.     

BCI-代数的余模糊理想

在BCI-代数中引入了余模糊理想的概念,讨论了它的某些性质,研究了BCI-代数的模糊理想和余模糊理想的关系.特别是,给出了一个如何由一个模糊子集生成一个余模糊理想和闭余模糊理想的过程.     

MV-代数的广义导子

借助于MV-代数的自同态引入并研究了MV-代数上的广义(→,⊕)-导子,得到了其等价刻画.此外,给出了MV-代数的广义中心主导子的概念,在此基础之上讨论了广义(→,⊕)-导子与MV-代数其它导子之间的关系,并利用强主中心广义导子的不动点集给出MV-代数成为Boole代数的等价刻画.所得结论推广了MV-代数上的导子,并借...     

BCI代数的Ω-犹豫模糊P理想

给定一个集合Ω,在BCI代数中引入Ω-犹豫模糊P理想的概念,讨论它的一些性质,研究了Ω-犹豫模糊P理想的同态像与同态原像的性质;研究了BCI代数中的Ω-犹豫模糊P理想与犹豫模糊P理想的相互构造,通过Ω-犹豫模糊P理想的水平P理想,讨论了BCI代数中Ω-犹豫模糊P理想的刻画;研究了Ω-犹豫模糊P理想与乘积型BCI代数的Ω-犹豫模糊P理想的关系.     

BCH-代数的闭模糊理想

引入了BCH-代数的闭模糊理想、子代数及优BCH-代数的概念,讨论它们的性质,获得若干结果。     

Semiring and Semimodule Issues in MV-Algebras

It is known that an atomic right LCM domain need not be a UFD but is a projectivity-UFD if it is also modular. This paper studies a slightly weaker and easier condition, the RAMP (acronym for the property in the title) , which also ensures that an atomic right LCM domain will be a projectivity-UFD. Among other things it is shown that in an atomic LCM domain, modularity is equivalent to the pair RAMP and LAMP (the left-right analog of RAMP). This result is then used to show that an atomic LCM domain with conjugation is modular. An example is given of an atomic LCM domain that has neither the RAMP nor the LAMP. All rings are not-necessarily commutative integral domains. Recall that an atomic ring is one in which every nonzero nonunit is a product of atoms (i.e. irreducibles) . A ring R is a right LCM domain if for any two elements a and b in R, aR ∩ bR is a principal right ideal. A right LCM domain need not be a left LCM domain [3] . If a ring has both properties it is called an LCM domain. It Is known (see Example 2 below) that, unlike the commutative case, an atomic right LCM domain need not be a UFD (unique factorization domain). In [1] it is shown that if the ring is also modular then it is a projectivity-UFD (definition of the latter recalled below)     

Top Varieties of Generalized MV-Algebras and Unital Lattice-Ordered Groups

In spite of the well-know fact that the system of ?-groups with strong unit (unital ?-groups) does not form a variety, there is a categorical connection between the category of unital ?-groups and the variety of generalized MV-algebras which enables us to naturally export equational machinery and terminology like “variety” from the latter category to the former.

Using this categorical equivalence, we study varieties, or equationally defined classes, and top varieties, varieties above the normal valued variety, of both structures. We generalize Chang's Completeness Theorem for generalized MV-algebras, and formulate some open questions for both structures.     

关于BL-代数的模糊滤子与模糊理想

在BL-代数中引入模糊超滤子和模糊固执滤子的概念,证明了如下条件对于BL-代数的非常数模糊滤子f来说是等价的:(1)f是布尔的和素的,(2)f是蕴涵的和素的,(3)f是超的,(4)f是固执的。应用模糊正蕴涵滤子给出G-代数的若干特征性质。提出BL-代数模糊理想的概念,给出一些重要例子,并通过例子说明在BL-代数中模糊理想一般不能由模糊滤子导出。同时,从模糊理想出发构造了商BL-代数,并建立了相应的同态基本定理。最后,研究了BL-代数的几类模糊理想及其相互关系,给出模糊布尔理想、模糊素理想、模糊超理想的特征性质。     

半群的模糊拟对称理想和它的根

本文定义了半群的模糊拟对称理想,研究了它和模糊素理想、模糊完全素理想之间的关系,并研究了它的根的特征     

Ideals and congruences in effect algebras and qmv-algebras

Ideals and sets of ideals of different types on QMV-algebras and the corresponding effect algebras are studied and compared.     

关于弱不可约的Fuzzy理想

给出弱不可约的Fuzzy 理想的定义,研究Fuzzy 理想是弱不可约的Fuzzy 理想的充分和必要条件。另外,讨论了弱不可约的Fuzzy 理想的同态象与同态原象的代数性质。     

关于W-Fuzzy格与W-理想

本文讨论了Ｆｕｚｙ格的Ｗ理想的一些基本性质。主要结果有：（１）对于一般的Ｆｕｚｙ格，给出了一个同余理想为Ｗ理想的若干充分条件和充要条件，所得结果是文［３］中相应结果在一般Ｆｕｚｙ格中的推广，从而完整地回答了文［３］中提出的一个问题；（２）对于Ｆｕｚｙ格下的同余素理想Ｐ，我们得到：Ｐ为Ｆ的Ｗ理想Ｆ／θ（Ｐ）为ＷＦｕｚｙ格；此时，Ｆ的的任一包含Ｐ的同余理想均为Ｗ理想。     

Complete Subobjects of Fuzzy Sets Over MV-Algebras

A subobjects structure of the category -FSet of -fuzzy sets over a complete MV-algebra is investigated, where an -fuzzy set is a pair A = (A, ) such that A is a set and : A × A is a special map. Special subobjects (called complete) of an -fuzzy set A which can be identified with some characteristic morphisms A ^* = (L × L, ) are then investigated. It is proved that some truth-valued morphisms are characteristic morphisms of complete subobjects.     

半群的模糊内理想

Abstract The concept of quasi-coincidence of a fuzzy interval value in an interval valued fuzzy set is a generalization of the quasi-coincidence of a fuzzy point in a fuzzy set. With this new concept, the interval valued （∈, ∈ Vq）-fuzzy interior ideal in semigroups is introduced. In fact, this kind of new fuzzy interior ideals is a generalization of fuzzy interior ideals in semigroups. In this paper, this kind of fuzzy interior ideals and related properties will be investigated. Moreover, the concept of a fuzzy subgroup with threshold is extended to the concept of an interval valued fuzzy interior ideal with threshold in semigroups.     

The Pointwise Characterizations of Fuzzy Ideals and Fuzzy Prime Ideals

TheconceptofthefuzzysubgroupsintroducedinRosenfeld[l],wasappliedtogeneralizesomeofthebasicconceptsofalgebra.In[2,3,4]LuWangjindefinedfuzzysubringsandfuzzyideals,introducedtheoperationsonfuzzyidea1s.In[5]theautherdiscussedaboutthenatureoffuzzysubringsbythenestedsubring.Butthepointwisedefinitionsoffuzzysubgroupsandfuzzysubringsarerare.Inthispaper,theautherprogramsanddiscussesthefuzzysubrings,fuzzyidealsandfuzzyprimeidealsbyfuzzyPoints..5l.PreliminariesLetusrecallsomeconceptsoccurrjnginthe[2,3…