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1、Ideals,VarietiesandAlgorithms,thirdeditionErrataforthesecondandsubsequentprintingsasofNovember29,2012Page15,line2ofDefinition1:“f/gandh/k”shouldbe“f/gandf′/g′”Page15,line3ofDefinition1:“kf=gh”shouldbe“g′f=gf′”Page27,Exercise11.b:“parta”shouldbe“part(a)”Page42,parts
2、(i),(ii)and(iii)ofProposition6:“GCD(f,g)”shouldbe“GCD(f,g)”(paren-thesesinwrongfont)(threeerrors)Page43,line12:“deg(r)>deg(r′)orr=0”shouldbe“deg(r)>deg(r′)orr′=0”Page47,line1ofExercise14.b:“(x−a)rl”shouldbe“(x−a)r1”11Page52,line1:“Werewritetheequationsbysubtracti
3、ngthexitermsfrombothsides”shouldbe“Werewritetheequationsbysubtractingthexitermsandconstantsfrombothsides”Page54,line−1:“Futhermore”shouldbe“Furthermore”Page55,line13:Addthesentence“Atotalorderisalsotransitive,sothatxα>xβandxβ>xγalwaysimplyxα>xγ.”Page60,line2ofExe
4、rcise1:“lm(f),lt(f)”shouldbe“lm(f),lt(f)”Page62,seconddisplay:“−y+1”shouldbe“−y+1”Page62,thirddisplay:Thelastthreelinesshouldbeasfollows(twoerrors):−y+1−y−12Page66,line6:“lt(p)5、i)≤multdeg(f)”Page66,line11:“30years”shouldbe“40years”Page67,line2:“lt(fi)”shouldbe“lt(f1)”Page68,line1ofExercise1:“orderset”shouldbe“orderedset”Page68,line1ofExercise7:“hf,f,fi=hx4y2−z,x4y2−z,x3y2−z,x3y3−1,x2y4−2zi”23shouldbe“hf,f,fi=hx4y2−z,x3y3−1,x2y4−2zi”(mul
6、tipleerrors)1231Page69,Exercise11.a:“β∈∆,ifandonlyifxα(i)dividesxβ,but”shouldbe“β∈∆ifandiionlyifxα(i)dividesxβand”Page72,firstdisplay:Thecommaattheendofthelastlineofthedisplayshouldbeaperiod.Page74,line1ofExercise10:“k[x1,...,xn,...,y1,...,yn]”shouldbe“k[x1,...,xn
7、,y1,...,yn]”Page74,line4ofExercise11:“α>uβ”shouldbe“α>uβ”Page74,line1ofExercise11.c:“u=”shouldbe“u=”Page76,line−8:“hlt(g1),...lt(gt)i”shouldbe“hlt(g1),...,lt(gt)i”Page77,line1:“hlt(g1),...lt(gt)i”shouldbe“hlt(g1),...,lt(gt)i”Page77,line−7:“x2∈h(lt(I)i”shouldbe“x2
8、∈hlt(I)i”Page78,line1:“Ag1+Bg2”shouldbe“Ag1+Bg2”Page80,Exercise4:“LM(g)”shouldbe“lm(g)”Page81,line2ofExercise15:“f1=f2=···0”shouldbe“f1=f2=···=0”Page82,line1of
