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1、Lattice-orderedRingsandModulesLattice-orderedRingsandModulesStuartA.SteinbergToledo,OH,USAStuartA.SteinbergDepartmentofMathematicsUniversityofToledoToledo,OH43601USAstuart.steinberg@utoledo.eduISBN978-1-4419-1720-1e-ISBN978-1-4419-1721-8DOI10.1007/978-1-4419-1721-8
2、SpringerNewYorkDordrechtHeidelbergLondonLibraryofCongressControlNumber:2009940319MathematicsSubjectClassification(2010):06F25,13J25,16W60,16W80,06F15,12J15,13J05,13J30,12D15©SpringerScience+BusinessMedia,LLC2010Allrightsreserved.Thisworkmaynotbetranslatedorcopiedin
3、wholeorinpartwithoutthewrittenpermissionofthepublisher(SpringerScience+BusinessMedia,LLC,233SpringStreet,NewYork,NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Useinconnectionwithanyformofinformationstorageandretrieval,electronicadapt
4、ation,computersoftware,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyarenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyar
5、esubjecttoproprietaryrights.Printedonacid-freepaperSpringerispartofSpringerScience+BusinessMedia(www.springer.com)ToDianeStephen,David,andJuliaPrefaceAlattice-orderedringisaringthatisalsoalatticeinwhicheachadditivetranslationisorderpreservingandtheproductoftwoposit
6、iveelementsispositive.Manyringconstructionsproducearingthatcanbelattice-orderedinmorethanoneway.Thistextisanaccountofthealgebraicaspectsofthetheoriesoflattice-orderedringsandofthoselattice-orderedmoduleswhichcanbeembeddedinaproductoftotallyorderedmodules—thef-modul
7、es.Itiswrittenatalevelwhichissuitableforasecond-yeargraduatestudentinmathematics,anditcanserveeitherasatextforacourseinlattice-orderedringsorasamonographforaresearcherwhowishestolearnaboutthesubject;thereareover800exercisesofvariousdegreesofdifficultywhichappearatth
8、eendsofthesections.Includedinthetextisalloftherelevantbackgroundinformationthatisneededinordertotomakethetheoriesthataredevelopedandtheresultstha
