OK. Well, first use: (a) use strict; (b) use warnings; (c) my variables.

Now, in your input loop you have:

  @t = split(/\t/, $_) ;
  $t[4]= $AB{[4]} ;
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  $AB{$alpha_numeric_field} = $numeric_field ;
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The output process contains:

  if ($var1[2] and exists $Ab{$var1[2]}) {
    print OUT "$var1[0]\t$var1[1]\t$var1[2]\t$AB[4]\n" ;
  }
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use strict would have picked up the $Ab{} mistake (undefined hash %Ab) and the use of $AB[4] (undefined array @AB). It would not, however, have picked up $AB{[4]}, which is the kind of honest-to-goodness inscrutability that Perl is justly famous for, and which one grows to be deeply fond of.

BTW, rather than:

  @var1 = split(/\t/,$_) ;
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  ($field_name, $other_field, $further_field, ...) = split(...) ;
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Thank you so very much!!! This worked like a charm. I cannot tell you how greatful I am. I knew it had to be something simple that my brain wasn't registering for some reason. Thank you again.

• For each record in file 1
  • break the record into fields
  • update a hash using Product Number and Produce Name as the keys, with a value of Univers ID

• For each record in file 2
  • break the record into fields
  • Is there a hash with Product Number and Produce Name as the keys?
    • If so, write out the keys and the value

I understand what you're saying but I still am unsure as to how the appropriate "UniversalID" values will be written along with the "ProductID" values. That is where my confusion is coming in.

minor update: I forgot to give the necessary admonition about strict and warnings, but I see that dwm042 has covered that below.

Here's some code that does basically what apl is suggesting (in the spirit of getting you started, but leaving some things for you to do to enhance the learning experience):

#! /usr/bin/perl

use strict;
use warnings;

my @file1 = (
             'A101 something 123',
             'A102 else 456',
             'A103 it 789',
             'A104 the 012'
            );

my @file2 = (
             'A102 else 456',
             'A103 it 789'
            );

my %prod_id;

foreach my $line ( @file1 ) {
  my( $num, $name, $id ) = (split /\s+/, $line);
  $prod_id{$num} = $id;
}

foreach my $line ( @file2 ) {
  my( $num, $name ) = (split /\s+/, $line);
  print "$num\t$name\t$prod_id{$num}\n";
}
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There is still a lot of work that you need to do with this. For example, to make it easy on myself, I take sample data from arrays, not files (you will need to fix that part). I also took some shortcuts by (1) always ignoring ProductName, (2) always assuming that the relevant ProductID exists as a key in the hash (this really needs to be checked at the point where I use $prod_id{$num} above).

As I said, this is not offered as a complete solution, rather as something to get you started.