You should work on your html before moving on to css... It's always best to decide which doc type your going to be using and specifying it at the top of your document.
Also, both ol and ul are block-level elements which means you do not need a div container around them unless you need it for additional positioning assistance... When coding xHTML/CSS you often get criticized if you don't do things just right and everyone has their own opinions... To minimize the threat of being criticized you need to learn good habits by coding efficiently with only the required markup, semantically, and when doing it for hire you must work swiftly.
Learn and memorize this URL by heart: http://validator.w3.org/
You'll be using that a lot until you have the routine things memorized.
Anyway, it depends how your using the code but it's probably better practice doing it like so:
PHP Code:
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<title>Untitled Document</title>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<style type="text/css">
#abc li {list-style:lower-alpha}
#object li {list-style:upper-alpha}
#object li li {list-style:decimal}
</style>
</head>
<body>
<ol id="abc">
<li></li>
<li></li>
<li></li>
</ol>
<ol id="object">
<li></li>
<li>
<ol>
<li></li>
<li></li>
<li></li>
</ol>
</li>
<li></li>
<li></li>
</ol>
</body>
</html>