Unformatted text preview: ab must be one of 1 , a, b ; however we can’t have ab = a or b , so this leaves ab = 1. Next a 2 = b . For a 2 must be one of 1 , a, b ; however a 2 = a ⇒ a = 0 or a = 1; also a 2 = 1 ⇒ a 21 = 0 ⇒ ( a1)( a + 1) = 0 ⇒ ( a1) 2 = 0 ⇒ a = 1; hence a 2 = b . Similarly b 2 = a . Consequently the multiplication table for F is × 1 a b 1 1 a b a a b 1 b b 1 a . (b) We use the addition and multiplication tables for F : A = 1 a b a a b b 1 1 1 1 a R 2 → R 2 + aR 1 R 3 → R 3 + R 1 1 a b a a a b a 10...
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This note was uploaded on 12/19/2011 for the course MAS 3105 taught by Professor Dreibelbis during the Fall '10 term at UNF.
 Fall '10
 Dreibelbis

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