Mini loop on static frontpage

I’m using a miniloop on my static frontpage.
This is the code for this miniloop:
<?
$news=$wpdb->get_results("SELECT ID,post_title FROM $wpdb->posts
WHERE post_status= \"publish\" ORDER BY 'ID' DESC LIMIT ".$how_many);
foreach($news as $np){
print ("<li><a href=\"");
echo get_permalink($np->ID);
print ("\">$np->post_title</a></li>");
}?>

This displayes the last 6 posts on my weblog in a small list. This is cool and works like a charm.

But, however, I would like to have displayed the most recent posts in a certain category (e.g. “Software”)

I tried adding the following code to that miniloop

WHERE post_status= \"publish\" AND post_category= \"Software\" ORDER BY 'ID' DESC LIMIT ".$how_many);

But that doesn’t work, it keeps displaying posts from all caterogies.

I went to my PHPadmin, and took a look at the wp_post table, and found that the column “post_caterogy” is always “0”, I guess that’s the reason why my code isn’t working…

How do proceed?