格蕴涵代数定义的简化

证明定义有二元运算→和零元运算(固定元)0的非空集合L(即:L是(2,0)型代数)只要满足四条算律就可成为格蕴涵代数.因此,在定义格蕴涵代数时,我们不必要求L是有界有余格,从L是(2,0)型代数出发即可,这样大大简化了格蕴涵代数的定义.     

局部R0-代数

文提出了局部R₀-代数的概念,并给出了相应的等价条件,即(i)R₀-代数L是局部的,(ii) ?x∈L,ord(x)<∞或ord(-x)<∞,(iii)每一个真滤子是primary.另外,我们又证明了任一R₀-代数是局部R₀-代数的子直积.     

关于Z-蕴涵代数

基于N-半单代数和格蕴涵代数、FI-代数, Wajsberg-代数、BCK-代数、BCI-代数、BCC-代数及MV- 代数等的关系[9],本文中,我们引入了Z-蕴涵代数的概念, 并讨论了它们的某些性质.     

利用格蕴涵代数找出所有LI-理想的方法

利用格蕴涵代数中理想的定义未找出所有的理想需要花费大量的时间.给出了利用格蕴涵代数的蕴涵运算表找出格蕴涵代数所有理想的方法;再利用析取运算表找出格蕴涵代数中所有sl_理想的方法;最后,利用蕴涵否运算表找出格蕴涵代数中所有LI-理想的方法.     

粗糙集代数与MV代数

讨论粗糙集代数与MV代数的关系以及由粗糙集代数构造MV代数的方法.粗糙集代数本身具有格结构,证明了在适当选取蕴涵及乘积运算之后,粗糙集代数就成为MV代数.     

格蕴涵代数的蕴涵表示定理

在对格蕴涵代数和模糊蕴涵代数研究的基础上,给出了格蕴涵代数的三个蕴涵表示定理。极大地简化了格蕴涵代数的定义形式,使得格蕴涵代数在形式上更加突出逻辑代数的特征及其与其它逻辑代数之间的联系与区别。为进一步研究格蕴涵代数及其与其它逻辑代数的关系提供了一个有力的工具。     

有限格蕴涵代数的零化子

研究有限格蕴涵代数的零化子,找出有限格蕴涵代数所有理想的零化子,并证明对有限格蕴涵代数的理想做零化子运算(记为0*)是一个逆序对合算子,因此在由有限格蕴涵代数L的所有理想所组成的集合∑(L)上定义一个蕴涵算子,则(∑(L),O,L,0*,)构成一个格蕴涵代数。     

正则Fuzzy蕴涵代数

Fuzzy蕴涵代数是 [0 ,1]值逻辑的蕴涵联结词的一种代数抽象。本文给出正则 Fuzzy蕴涵代数的几个刻画 ,并且得到正则 Fuzzy蕴涵代数构成格的几个条件。     

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     

粗糙集代数中的剩余格结构

讨论粗糙集代数与剩余格的关系.借助近似代数上的原子及同余关系,证明了在适当选取蕴涵算子及相应的剩余算子之后,粗糙集代数就成为剩余格,并进而证明了粗糙集代数也是MV代数与R0代数.     

On the Product and Factorization of Lattice Implication Algebras

In this paper,the concepts of product and factorization of lattice implication algebra areproposed,the relation between lattice implication product algebra and its factors and some properties oflattice implication product algebras are discussed.     

Symmetric Brace Algebras

We develop a symmetric analog of brace algebras and discuss the relation of such algebras to L_∞-algebras. We give an alternate proof that the category of symmetric brace algebras is isomorphic to the category of pre-Lie algebras. As an application, symmetric braces are used to describe transfers of strongly homotopy structures. We then explain how these symmetric brace algebras may be used to examine the L_∞-algebras that result from a particular gauge theory for massless particles of high spin.Mathematics Subject Classifications (2000) 55S20 (primary), 70S15 (secondary).Tom Lada: The research of the first author was supported in part by NSF grant INT-0203119.Martin Markl: The research of the second author was supported by grant MŠMT ME 603 and by the Academy of Sciences of the Czech Republic, Institutional Research Plan No. AV0Z10190503.     

Free Algebras in Certain Varieties of Distributive Pseudocomplemented De Morgan Algebras

In this paper we characterize the join irreducible elements of the free algebras on n free generators in the subvarieties of the variety V₀ of pseudocomplemented De Morgan algebras satisfying the identity xx′* = (xx′*)′*.     

On Certain Filters in Lattice Implication Algebras

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Projective Modules Over Frobenius Algebras and Hopf Comodule Algebras

This note presents some results on projective modules and the Grothendieck groups K ₀ and G ₀ for Frobenius algebras and for certain Hopf Galois extensions. Our principal technical tools are the Higman trace for Frobenius algebras and a product formula for Hattori-Stallings ranks of projectives over Hopf Galois extensions.     

Prime Space of Lattice Implication Algebras

1.IntroductionPeoplehavepaidmoreattentiontolathcevaluedlogicsystem,whichwillbecomemuchbetterlogicalsystemforintelligentcomputer.InreferenceL1JXuYangpresentanalgebrastructure-latticeimplicationalgebrabycomblngthelatticewithimplicationalgebraastruevaluefieldoflatticevaluedlogicaIsystem.Afterthat,westudytheimplicationhomomor-phism,congruencerelationsandalgebraicstructureoflatticeimplicationalgebraanddiscussthefirstorderlogicalsystemFMbasedonlatticeimplicationalgebras,andobtainedseveralimpor-ta…     

Standardly Stratified Extension Algebras

Abstract

The paper generalizes some of our previous results on quasi-hereditary Koszul algebras to graded standardly stratified Koszul algebras. The main result states that the class of standardly stratified algebras for which the left standard modules as well as the right proper standard modules possess a linear projective resolution – the so called linearly stratified algebras – is closed under forming their Yoneda extension algebras. This is proved using the technique of Hilbert and Poincaré series of the corresponding modules.

     

模糊格蕴涵代数范畴

本文提出了模糊格蕴涵代数范畴FLC的概念，讨论了它的一些基本性质并指出了它与范畴LC的关系．