On Certain Filters in Lattice Implication Algebras

ＯｎＣｅｒｔａｉｎＦｉｌｔｅｒｓｉｎＬａｔｔｉｃｅＩｍｐｌｉｃａｔｉｏｎＡｌｇｅｂｒａｓＬｉｕＪｕｎ；ＸｕＹａｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＳｏｕｔｈｗｅｓｔＪｉａｏｔｏｎｇＵｎｉｖｅｒｓｉｔｙ，Ｃｈｅｎｇｄｕ，...     

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…     

Fuzzy Ordered Filters in Implicative Semigroups

Animplicativesemilatticeisanalgebraicsystemhavingasmodelslogicalsystemsequippedwithimplicationandconjunction,butnotpossessingadisjunction.ImplicativesemilatticeswerestudiedbyW.C.Nemitz[5].In[2],T.S.BlythgeneralizedsomeresultsofW.C.Nemitz[5]byintroducingthenotionofaBrouweriansemigroup.FollowingtheideasofNemitzandBlyth,M.W.ChanandK.P.Shum[3]introducedthenotionofnegativelypartiallyorderedimplicativesemigroupsandgeneralizedsomeresultofNemitzonimplicativesemilatticestoim-plicativesemigroups…     

Some Characterizations of Nil Ideals in BCI—algebras

51.IntrodcutionIn[1j,thenotionsofnilidealinBCI-algebrasandinlBCI-algebrawereintreduced.WeshowthatnilBCI-algebraisageneralizationofassociativeandquasi-associativeBCIalgebra([2J,[3j).lnthispaper,somecharacterizationsofnilidealsinBCI-algebraswereproved.Moreover,theBCI-algebrassatifyingO*x.=xwerediscussedandvariousproPertieswereproved.Werecallsomedefinitionsande1ementaryproperties.ThefollowingsaretrueinaBCI-al-gebra:(l)x o=x;(2)(x*y)*z=(x z) y;(3)x相似文献   

Generators of Rings of Differential Operators on a Class of k—algebras

51.IlltroductionSmithL4JproPoseaso1vingprocedure,whichcIcternllnesl1olyno[nialresolutlonofI3:lrt1itldifferentialequationcorrespondingbysomecoordinateringsofirreduciblel7l;lnecurves.-I'l1lsprogrameventual1ydependsontl1edeterminationofgeneratorsofringsofdif…     

Complete Positivity of Elementary Operators on C^＊—algebras

1.IntroductionandPreliminariesInthispaper,AdenotesaC'-algebra.AnelementaryoperatoronAisamappingoftheformE:x-Zaixbi,whereaiandbiarefixedelementsofA.AnidempotenteinAiscalledi-lminimal,ifeAe=Ce.ThesocleofA,soc(A)isdefinedtobethetwo-sidedidealgeneratedbyallminimalidempotentsinAoroiftherearenone.AissaidtObeprimeifxAy=Oimpliesx=oory=oforallx,yinA.Aiscalledprimitiveifithasafaithfulirreduciblerepresenta-tion.LetAandBbeC'-algebras,alinearmap@:A-Biscalledpositiveifdi(a)ispositiveforallPositiv…     

On the Structure of the B—cocleft Module Coalgebra

§１．　ＴｈｅＥｑｕｉｖａｌｅｎｔＴｈｅｏｒｅｍｏｆｔｈｅＣｒｏｓｓｅｄＣｏｐｒｏｄｕｃｔＬｅｔＣｂｅａｌｅｆｔＨ－ｗｅａｋｌｙｃｏｍｏｄｕｌｅｃｏａｌｇｅｂｒａ［４］ｗｉｔｈｔｈｅｓｔｒｕｃｔｕｒｅρ－Ｃ（ｃ）＝∑ｃ（１）ｃ（２）．ＤｂｅｌｅｆｔＨ－ｍｏｄｕｌｅｃｏａｌｇｅｂｒａ［２］ｗｉｔｈｔｈｅｓｔｒｕｃｔｕｒｅ“”．Ｆｏｒα∈Ｈｏｍκ（Ｃ，ＨＨ）ｄｅｎｏｔｅα（ｃ）＝∑α１（ｃ）α２（ｃ）．Ｄｅｆｉｎｅ△－：ＣＤ→（ＣＤ）（ＣＤ）ａｎｄε－：ＣＤ→κａｓｆｏｌｌｏｗ－ｉ…     

Completely Positive Definite Maps Over Topological^＊—algebras

ＣｏｍｐｌｅｔｅｌｙＰｏｓｉｔｉｖｅＤｅｆｉｎｉｔｅＭａｐｓＯｖｅｒＴｏｐｏｌｏｇｉｃａｌ－ａｌｇｅｂｒａｓＸｕＴｉａｎｚｈｏｕ（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＢｅｉｊｉｎｇＩｎｓｔｉｔｕｔｅｏｆＴｅｃｈｎｏｆｏｇｙ，...     

Pro—C^＊—代数中的次正规元

探讨了Pro-C^*-代数中的次正规元,给出了具有余等距对Pro-C^*-代数中次正规元的一个代数特征。     

伪补MS-代数的滤子同余关系

在伪补MS-代数上引入余核滤子和完全滤子的概念,研究伪补MS-代数的余核滤子和完全滤子的性质,获得了余核滤子和完全滤子生成的同余关系的表达式,证明了具有余核滤子的最小同余关系有同余一致性.     

On symmetric extended MS-algebras whose congruences are permutable

Algebras whose congruences are permutable were investigated by a number of authors in the literature. In this paper, we study the symmetric extended MS-algebras whose congruences are permutable. Some results obtained by Jie Fang on symmetric extended De Morgan algebras are generalized.     

Fixed point separating congruences on double MS-algebras

Here we show that there exists a greatest fixed point separating congruence denoted by Ψ on a double MS-algebra (L;^{0, +}). Some properties of Ψ under certain conditions on fixed point complete and fixed point distributive have also been described. An aid research grant from the State Education Commission of China is gratefully acknowledged     

剩余格中的滤子

This paper is devoted to the discussion of filters in residuated lattices. Some equivalent conditions about filter were given. The structure of generated filter was established. The concept of implicative filter in residuated lattice was proposed with its basic properties being discussed.     

关于剩余格中滤子的格结构

This paper is devoted to the discussion of filters in residuated lattices. The lattice structure of filters in residuated lattice was established. It is proved that the set of all filters forms a distributive lattice. Also, the concept of prime filter in residuated lattice was proposed and some equivalent conditions about prime filter were given.     

On Special Implicative Filters

In her well-known book, Rasiowa states without proof that in implicative algebras there is a one-to-one correspondence between kernels of epimorphisms and the so-called special implicative filters, and that in the logic whose algebraic counterpart is the class of implicative algebras the deductive filters coincide with the special implicative filters. We show that neither claim is true, and how to repair the situation by redefining some of the notions involved. We answer other questions concerning special implicative filters, taking the theory of algebraizable logics of Blok and Pigozzi as a framework to approach the question in a systematic way.     

伪补MS-代数的同余关系

本文研究了伪补MS-代数的同余关系.利用正则滤子和伪补代数的对偶窄间理论,得到了正则滤子所生成的同余关系的性质以及同余可换的伪补MS-代数类,从而推广了文献[9]的结果.     

On Orthogonal Double Covers of Graphs

A transformation which allows us to obtain an orthogonal double cover of a graph G from any permutation of the edge set of G is described. This transformation is used together with existence results for self-orthogonal latin squares, to give a simple proof of a conjecture of Chung and West.     

On Orthogonal Double Covers of Graphs

An orthogonal double cover (ODC) is a collection of n spanning subgraphs(pages) of the complete graph K _n such that they cover every edge of the completegraph twice and the intersection of any two of them contains exactly one edge. If all the pages are isomorphic tosome graph G, we speak of an ODC by G. ODCs have been studied for almost 25 years, and existenceresults have been derived for many graph classes. We present an overview of the current state of research alongwith some new results and generalizations. As will be obvious, progress made in the last 10 years is in many waysrelated to the work of Ron Mullin. So it is natural and with pleasure that we dedicate this article to Ron, on theoccasion of his 65th birthday.