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73 GraduTaetxeti sn Mathematics EditorBioaalr d S.A xlerF .W.G ehrinKg. AR.i bet Springer NewY ork Berlin Heidelberg HongK ong London Milan Paris Tokyo ThomaWs.H ungerford ALGEBRA Springer Thomas Hungerford W. DepartmeonfMt a thematics ClevelaSntda tUen iversity ClevelaOnHd 4,4 115 USA EditBoorairadl S.A xler Gehring K.A.R ibet F.W. MathematDiecpsa rtment MathematDiecpsa rtment MathematDiecpsa rtment SanF ranciSstcaot e EasHta ll UniversoifCt ayl ifornia, University Universoift yM ichigan Berkeley SanF rancisCcAo 9,4 132 AnnA rborM,I 48109 BerkelCeAy ,9 4720-3840 USA USA USA [email protected] fgehr@in g [email protected] erkeley.edu maths.a u.m ich.edu I MathematSiucbsj eCclta ssification (200206)-:0 1 LibraorfyC ongreCsast aloging-in-PuDbaltiac ation HungerfoTrhdo,m as W. Algebra Bibliograpp.h y: AlgebrIa. T it ie 1. QA .H3 73-15693 1558 512 ISBN Printoenda cid-fpraepee r. 0-387-90518-9 ISBN 3-540-90518-9 1974S pringer-VNeerwl Yaogr kI,n c. © Allr ighrtess ervTehdi.ws o rkm ayn otb et ransloart ecdo piinew dho loer i np arwti thotuhtew ritten permissoifot nh e publ(iSsphreirn ger-NVeerwl Yaogr kI,n c.1,7 5F iftAhv enueN,e w YorkN,Y USA)�e xcepfto rb rieefx cerpitncs o nnectwiiotnhr evieowrss cholaarnlayl ysUisse.i n 10010, connectwiiotnh a nyf ormo fi nformatsitoonr aagned r etrieevlaelc,� onaidca ptatcioompnu,t er softwaorreb ,y similar or mdeitshsoidmoilnlooagwryk nowno rh ereafdteevre lopiesfd o rbidden. Theu sei nt hipsu blicaotfit orna dnea mestr,a demarks, smearrvkisac,ne ds imiltaerr mesv,e ni ft hey aren oti dentiafsis eudc hi,sn ott ob et akeans a ne xpressoifoo pni niaons t ow hetehro rn ott heayr e subjecptr opriertiagrhyt s. to Printetdh eUi nni teSdt atoefsA merica.( ASC/SBA) 15 141 3 SPIN 11013129 SpringVeerr-laigsa parotf SpringSecri enBcues+i neMsest fia springeronline.com ToM ary tot he Preface SprinEgdeirt ion Ther eceptgiiovne tno t hefi rst edition oifn dicattheasit s h asfi llead Algebra defininteee d: prtoov iad see lf-contoanien-evdo,l ugmrea,d ualteev eall gebtreax t thaitsr eadabblyte h ea veraggrea duastteu deanntd f lexiebnloeu gtho a ccomodate a widev arieotfyi nstructaonrdsc oursceo ntenStisn.c iet h asb eens ow ell re ceiveadn,e xtensirveev isiaottn h itsi med oesn ots eemw arrantTehde.r efore, nos ubstancthiaanlg ehsa veb een maidnte h et exfto rt hirse visperdi ntiHnogw. evera,U k nownm isprianntdse rrors hbaeveen c orrectaendd s everparloo fsh ave beenr ewritten. I gratetfouP la ulH almosa nd Gehrinagn,d t heS pringsetra fff,o r am F.W . theiern couragemeanntda ssistainnbc rei ngionugt tehdiist iIotni .sg ratiftyoi ng knowth at wilclo ntintuoeb ea vailatbolt eh em atheamticcaolm munity. Algebra SpringVeerr-laigst ob ec ommendefdo ri twsi llingnetosc so ntintuoep roduce higqhu alitmya themattiecxsta sta timweh enm anyo thepru blishaerrels o oking tol esesl egabnuttm orel ucratvievnet ures. SeattWlaes,h gitnon THOMAS W. HUNGERFORD June1,9 80 A numberof c orrectwieorneis n corporaitnte hdef ifth Notoent htew elfptrhi nt(i2n0g0 3): printJit nhganktsot hes harp-edyieldi geonfGc ee orgBee rgmaann dh iss tudenattBs e rkeley and KeqinF engo ft heC hinesUen iversoiftS yc ienacned T echnoloAgdyd.i tional corrections appear int hipsr intitnhga,n ktso V ictor BoByokboC ,a cioppJoo,e Mott,R oberJto lya,n dJ oe L. Brody. vii -.