Let A be the 10-adic numbers. Prove that there are two elements a, b EA of...

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Let A be the 10-adic numbers. Prove that there are two elements a, b EA of A such that a a #0 and b #0 7 ab=0 . [Notice that this means that A is not a field, because if ab=0 then 2 but 0 and b can't have multiplicative inverses: ab: <=0 means 1/a(ab) = 01 which means ₂ b=0 J Let A be the 10-adic numbers. Prove that there are two elements a, b EA of A such that a a #0 and b #0 7 ab=0 . [Notice that this means that A is not a field, because if ab=0 then 2 but 0 and b can't have multiplicative inverses: ab: <=0 means 1/a(ab) = 01 which means ₂ b=0 J

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To prove that there are two elements a b A such that a 0 and b 0 but ab 0 we can consider the 10adic ... View the full answer