If you downloaded installation files to your Windows computer, you have Windows installation files and serial number which are not going to work on a Mac computer.
If you had purchased 11 in box packaging, you would have gotten 2 installation discs, one for Windows and one for Mac. Since that does not appear to be the case, I would answer that you are facing purchasing Premiere Elements Mac for your Mac computer.
Thanks for the reply. I had hoped that adobe would allow me to re-download the Elements 11 which I had purchased from there website, the serial number is in my account information.