you could ditch the temporary variable altogether..

#!/usr/bin/perl
use strict;

my %alink;

# Create some arrays of random numbers...
foreach my $name ('Fred', 'Barney', 'Wilma', 'Peggy'){
  for (my $i = 0; $i < 5; $i++){
    push( @{$alink{$name}}, int(rand(30)) );
  }
}

foreach my $key (keys %alink){
  foreach my $element ( @{$alink{$key}} ){
    print $key,' ',$element,"\n";
  }
}
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(also added 'use strict;' and then 'my' declarations as required.)