Unformatted text preview: { ( 2 a , 2 b )  a , b ∈ Z } (c) { ( 2 a , )  a ∈ Z } (d) { ( a ,a )  a ∈ Z } Let the relevant set of elements be I . (a) No. For example ( 1 , 1 ) ∈ I , but ( 1 , 1 )( 1 , ) / ∈ I . (b) Yes. 0 ∈ I and I is closed under +. Finally if ( x , y ) ∈ Z × Z , then ( 2 a , 2 b )( x , y ) = ( 2 ax , 2 by ) ∈ I . (c) Yes. 0 ∈ I and I is closed under +. Finally if ( x , y ) ∈ Z × Z , then ( 2 a , )( x , y )=( 2 ax , ) ∈ I . (d) No. For example ( 1 ,1 ) ∈ I , but ( 1 ,1 )( 1 ,1 ) = ( 1 , 1 ) / ∈ I ....
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This note was uploaded on 01/02/2012 for the course MATH 4124 taught by Professor Staff during the Spring '08 term at Virginia Tech.
 Spring '08
 Staff
 Math, Algebra

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