If you're a Creative Cloud subscriber, you don't need a serial number to activate and use your Adobe apps. Your subscription includes all the features and updates in the latest versions of your apps. You can install and use as many copies of your apps as you want on all your personal computers. Just sign in with your Adobe ID to activate them.
If you're not a Creative Cloud subscriber, you can buy an app from Adobe or a reseller and use it indefinitely with a perpetual license (with no expiration date). To activate and use these apps, you need a valid serial number.