廣義冪級(jí)數(shù)環(huán)及其模的若干問(wèn)題.pdf

1、福建師范大學(xué)碩士學(xué)位論文廣義冪級(jí)數(shù)環(huán)及其模的若干問(wèn)題姓名：肖民卿申請(qǐng)學(xué)位級(jí)別：碩士專(zhuān)業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：薛衛(wèi)民辛林2001.6.5AbstractSincethe90’SOtthe20thcenturybecauseoftheexcellentresearchbyPRiben—boim，LiuZhongkuiete，peoplehavemademoreunderstandingfortheringsofgeneralizedpower

2、seriesTheringsofgeneralizedpowerseriesareattractingscholars’moreandmoreinterestInthisthesis，wealsostudytheringsofgeneralizedpowerseriesandthemodulesoverthemInthefirstpart‘’Preliminaries”weintroductsomerelatedconcepts，for

3、exampleorderedsetsmonoidsorderedmonoidsetcandalsobasicfactsabouttherings[[R5j】]ofgeneralizedpowerseriesInsection2，westudytheidealsofringsofgeneralizedpowerseriesWeprovethetwoformulae：“[[(R。)5!]】=[In5’!]】_c。”and。‘[[(R／，)5

4、，!]】竺[[R5，511／[[18，5]]”Then，wediscusstwopairsofidealsThefirst，[[以。!】]and圻f萬(wàn)葡Weknowthat，ifSisastrictlytotalorderedmonoidthen枷萬(wàn)可∈[[47s11，but”D一”isnotlIpWeobtaintwosufficientcondictionsof”、／i曠葡≥[[以^!”Furthermore，wegivetwela

5、tedpropertiesWediscuss[[Nil(R)5，釧andNil([[Rs]])Therearetwosufficientcondictionsfortheequality“[(Ⅳif(R)5，】]=Nil([[Rs】])”Insection3wemakecharacterizationsofidempotentsoftheringsofgeneralizedpowerserieswithsomeadditionalcon

6、ditions，andsequentiallygivecharacter—izationsofprimitiveidempotentsandlocalidempotentsWealsogiveaequivalentconditionfor“陋5’(】】tobeanormalring”andaequivalentconditionfor“[In5，]】tobealocalring”Section4containssomesufficien

7、tcondictionssuchthat[[R5，]]isa71regularringThelastsectionofthepapertalksabouttheleft[[R5，釧一moduleM[S】whichwasconstructedbyLiuin[11]First，weconsidertheassociatedprimeidealsofM[SJWeproofthat[IF5’(]】isanassociatedprimeideal

8、sofM[S]ifandonlyifPisanassociatedprimeidealsofMThesecondoneistheprimesubmodulesofM舊WeobtainthatifN[S】isaprimesubmodulesofM吲，thenNisaprimesubinoduleofMButtheconverseiSnottrueKeywords：Orderedmonoidringofgeneralizedpowerser