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Unformatted text preview: [ a ] 6 = [ a ] 3 , where a Z is arbitrary. Suppose [ a ] 6 = [ b ] 6 . Then 6  ( ab ) , hence 3  ( ab ) and we deduce that [ a ] 3 = [ b ] 3 . Thus if we write [ a ] 6 in different ways, we always get the same result when we apply the given formula for . Therefore is welldened. (b) Let a , b Z . Then ([ a ] [ b ]) = [ a + b ] = [ a + b ] = [ a ] [ b ] = [ a ] [ b ] . (c) [ a ] ker if and only if [ a ] 3 = [ ] ; that is if and only if 3  a . Therefore ker consists of the elements of the form [ a ] 6 where 3  a , in other words { [ ] , [ 3 ] } ....
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This note was uploaded on 01/02/2012 for the course MATH 3124 taught by Professor Parry during the Fall '08 term at Virginia Tech.
 Fall '08
 PARRY
 Math, Algebra

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