含有中间幂等元满足同余条件的◇-富足半群

《含有中间幂等元满足同余条件的◇-富足半群》由会员上传分享，免费在线阅读，更多相关内容在行业资料-天天文库。

1、数学杂：，I：．、Vo1．31(2011)J．ofMath．(PRC)NO．6◇一ABUNDANTSEMIGRoUPSWITHAMEDIALIDEMPoTENTSATISFYINGTHEC0NGRUENCECoNDITIoNLIYong—hua，FUWen(sc。。lG￡^e"8ticalSciences，SothChi佗aNorm口?University，Guangzh。510631，ChiG)Abstract：Inthisarticle，weintroduceGreen’S◇一relationsando-abundantsemigroupsandstudytheo-abundantsem

2、igroupswithamedialidempotent，satisfyingthecongruencecondition-Byusingidempotent—generatedregularsemigroupswithamedialidempotentando-quasiadequatesemigroups，weestablishaconstructionofsuchsemigroups-Keywords：o-abundantsemigroup；congruencecondition；medialidempotent2010MRSubjectClassification：20M10Docu

3、mentcode：AArticleID：0255—7797(2O11)O6—1O15-O9In『11．BlythandMcFaddenestablishedtheinternalstructureofnaturallyorderedreg／ularsemigroupsthathaveagreatestidempotent．In1983，they【2]obtainedamethodforconstructingallregularsemigroupswithanormalmedialidempotent．Loganathan[11】DrOVedthatBlyth—McFadden’Smetho

4、dwithminormodifications，alsoobtainedadescriptionofregularsemigroupwithamedialidempotent．Inthecaseofregularsemigroupstheyuseidempotent—generalizedregularsemigroupswithamedialidempotentandorthodoxmonoidstoconstructtheregularsemigroupswithamedialidempotent．E1一Qallali[3]extendedthatconstructiondescribe

5、din【2]toaclassofabundantsemigroupswithanormalmedialidem—potent．LaterJingf12】characterizedabundantsemigroupswithamedialidempotent．Inthecaseofabundantsemigroupstheauthorestablishedtheabundantsemigroupswithamedialidempotentbyidempotent—generalizedregularsemigroupswithamedialidempotentandquasi—adequate

6、monoids．Inthispaperouraimistoobtainaconstructionofo-abundantsemigroupwithamedialidempotentthatsatisfiesthecongruencecondition，whichgeneral-izesthecorrespondingresultsin[2]，[11]，[3]and[12]．InSection1，wefirstintroduceGreen’S~~relations(C。，冗。)ando-abundantsemigroupsandthengiveanexamplewhichis◇一abundan

7、tsemigroupsuchthatCC。Cand冗冗。．InSection2，wediscussindetailthepropertiesofmedialidempotentsinae-abundantsemigroup．Section3describesaconstructionofo-abundantsemigroupswithamedia1idempotentthatsatisfiesthecongr