格蕴涵代数与BCK代数的关系

本文给出了有界可换的ＢＣＫ代数的分配性的一些等价条件，指出了格蕴涵代数与有界可换分配的ＢＣＫ代数以及格Ｈ蕴涵代数与有界关联的ＢＣＫ代数之间的对偶关系     

格蕴涵代数的BCK代数的关系

本文给出了有界可换的ＢＣＫ代数的分配性的一些等价条件，指出了格蕴涵代数与有界可换分配的ＢＣＫ代数以及格Ｈ蕴涵代数与有界关联的ＢＣＫ代数之间的对偶关系。     

正定关联BCI—代数

本文是作者［１］和［２］的继续，引入了正定关联ＢＣＩ－代数的概念，并证明了：正定关联ＧＢＣＫ－代数类和Ｐ－半单ＢＣＩ－代数类是正定关联ＢＣＩ－代数类的真子类。     

BCK和BCI—代数的映射

在ＢＣＫ－代数中引进了一个右映射和ＢＣＩ－代数中引进了一个弱左映射，并探讨它们的性质。从而推广了文［１］中大部分结果。主要结果是：如果Ｘ是一个ＢＣＫ－代数，Ｙ是一个正定关联ＢＣＫ－代数，则所有Ｘ到Ｙ的左映射的集合也构成一个正定关联ＢＣＫ－代数。     

可交换的Fuzzy蕴涵代数

Ｆｕｚｙ蕴涵代数,简称ＦＩ代数,是一个新的代数系统,它是［０,１］值逻辑的蕴涵连接词的代数抽象。本文在ＦＩ代数中引进“交换”运算,从而得到了进一步刻划ＦＩ代数及ＨＦＩ代数的若干结果。本文还证明了交换ＦＩ代数关于偏序≤是一个格     

PFI代数及其P滤子

文「１」引入了ＦＩ代数及其滤子，文「２」讨论了ＦＩ代数与ＭＶ代数的联系，本文在此基础上引入了正关联ＦＩ代数及其正关联滤子，并得到几个重要性质。     

BCI—代数的KI并代数

本文引入ＢＣＩ－代数的ＫＩ并代数，它是ＢＣＫ－代数的无交并的推广。     

关于单BCI－代数的一些结果

本文讨论了单ＢＣＩ－代数．证明了一个ＢＣＩ－代数是单的当且仅当它的子代数都是单的；给出了单ｐ－半单ＢＣＩ－代数的一种表示式；证明了一个ｐ－半单ＢＣＩ－代数是单的当且仅当它的阶是素数；这样得到了一批（无限多个）单ＢＣＩ－代数；证明了商ＢＣＫ－代数Ｘ／Ａ是单的当且仅当Ａ是Ｘ的极大理想．     

BCI—代数和弱半联理想

引进ＢＣＩ－代数的弱关联理想的概念，并用以刻划弱关联ＢＣＩ－代数，从而推广了文［３］中的的一上结结论。     

BCI—代数的Fuzzy强蕴涵理想

本文引入了ＢＣＩ－代数的强蕴函理想的概念，研究了它的性质，同时讨论了ＢＣＩ－代数中的Ｆｕｚｚｙ关系。     

Bounded BCK‐algebras and their generated variety

In this paper we prove that the equational class generated by bounded BCK‐algebras is the variety generated by the class of finite simple bounded BCK‐algebras. To obtain these results we prove that every simple algebra in the equational class generated by bounded BCK‐algebras is also a relatively simple bounded BCK‐algebra. Moreover, we show that every simple bounded BCK‐algebra can be embedded into a simple integral commutative bounded residuated lattice. We extend our main results to some richer subreducts of the class of integral commutative bounded residuated lattices and to the involutive case. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

关于格蕴涵代数与BCK-代数

证明了格蕴涵代数与有界可换 Ｂ Ｃ Ｋ代数是两类相互等价的代数系统,借此得到了一类 Ｂ Ｃ Ｋ代数的结构定理     

赋范BCK-代数与模糊BCK-代数

在BCK－代数中引入范数的概念,给出赋范BCK－代数中的一些基本结果,讨论了有界赋范BCK－代数与模糊BCK－代数的一些联系。     

Negation and BCK‐algebras

In this paper we consider twelve classical laws of negation and study their relations in the context of BCK‐algebras. A classification of the laws of negation is established and some characterizations are obtained. For example, using the concept of translation we obtain some characterizations of Hilbert algebras and commutative BCK‐algebras with minimum. As a consequence we obtain a theorem relating those algebras to Boolean algebras.     

蕴涵代数与BCK代数

系统研究 Fuzzy蕴涵代数与 BCK代数之间的关系 ,给出 MV代数与 BCK代数之间的联系 ,建立正则 FI代数和对合 BCK代数的对偶代数     

The Semigroup Characterizations of Positive Implicative BCK—algebras

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＢｙａＢＣＩ－ａｌｇｅｂｒａｗｅｍｅａｎａｎａｌｇｅｂｒａ（Ｘ，，０）ｏｆｔｙｐｅ（２，０）ｗｉｔｈｔｈｅｆｏｌｌｏｗｉｎｇｃｏｎｄｉ－ｔｉｏｎｓ：（１）（（ｘｙ）（ｘｚ））（ｚｙ）＝０；（２）（ｘ（ｘｙ））ｙ＝０；（３）ｘｘ＝０；（４）ｘｙ＝ｙｘ＝０ｉｍｐｌｉｅｓｘ＝ｙ．ＩｆａＢＣＩ－ａｌｇｅｂｒａ（Ｘ，，０）ｓａｔｉｓｆｉｅｓ（５）０ｘ＝０．ｔｈｅｎｉｔｉｓｃａｌｌｅｄａＢＣＫ－ａｌｇｅｂｒａ．ＩｎａＢＣＩ－ａｌｇｅｂｒａ，ｔｈｅｆ…     

BCK—代数的模糊理想的若干性质

运用模糊点的概念研究BCK代数的模糊理想等一些基本概念和性质,建立它与利用隶属函数和水平截集等常见刻画方式之间的关系。     

关于BCK代数的模型论性质

This paper is devoted to the study of the logical properties of BCK algebras. For formalized BCK algebra theory T, it is proved that T is preserved under submodels and unions of chains; T is neither complete nor model complete, and hence there exist no built-in Skolem function. Moreover, the ultraproduct BCK algebras and the fuzzy ultraproduct of fuzzy subsets of BCK algebras were proposed by using the concept of ultrafilters with corresponding properties of fuzzy ideals discussed.     

Local pseudo-BCK algebras with pseudo-product

Pseudo-BCK algebras were introduced by G. Georgescu and A. Iorgulescu as a generalization of BCK algebras in order to give a corresponding structure to pseudo-MV algebras, since the bounded commutative BCK algebras correspond to MV algebras. Properties of pseudo-BCK algebras and their connections with other fuzzy structures were established by A. Iorgulescu and J. Kühr. The aim of this paper is to define and study the local pseudo-BCK algebras with pseudo-product. We will also introduce the notion of perfect pseudo-BCK algebras with pseudo-product and we will study their properties. We define the radical of a bounded pseudo-BCK algebra with pseudo-product and we prove that it is a normal deductive system. Another result consists of proving that every strongly simple pseudo-hoop is a local bounded pseudo-BCK algebra with pseudo-product.     

不分明化PCK—代数

在BCK－代数中定义了不分明化子代数和不分明化理想的概念,讨论了它们的性质及彼此间的关系。