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absalg_ex3b - (40 pts Consider the ring R = Q[x(3:3-~ $2(a...

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Unformatted text preview: . (40 pts.) Consider the ring R = Q[x]/ (3:3 -~ $2). (a) Expreas the product ($2 + 72:)(332 + 32:) in R in its simplest form. V: 3% ‘5’; - w “3 ”a we 2": ’ ”é“ méfléfagmgdiix Wi~ {if X Z; {4: X 3%“ 3:}? < k: '5 a“; ff” 2% 2 ”if. \ HR I MW xx... 41;?» fit ’ ”’8 57:. in“ 2/5 £2 4. (30 pts.) Consider the ring: Z3{m, y] / (5132, my, ya). (a) How many elemenis are there in this ring? Expiain your answer} .W E g g 5 52A— 5; ”My; figma :5}? w}: 3w?” mg:- 2;,” M :5 l .f A > :2 ;; y= :KJ g.. 3A LA F ”a. my: “a imam a? H; . ? gfi/sfimw (b) Write the product (1 —£— x + y)(2 —E— yfinasimplest form. #1 “2:: g :3 ...
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