Jmkaden
According to the Adobe information, you can have your purchased serial number (activated) on no more than two of your computers. And, not run at the same time.
QuickTime is a requirement for Premiere Elements and both need to be run from a User Account with Administrative Privileges. All well and good for the personal computer not used at work. But, what control does the company have over the Window 8 tower? Will you be able to run Premiere Elements on that Windows 8 tower from a User Account with Administrative Privileges (maybe even requiring Run As Administrator)?
ATR
