No. The serial number will only apply to the single version you buy. However, you can and certainly should download the the trial version of 2021 for testing on your computer. So far, other than a few features, they both are running without trouble on my Windows laptop.
Thanks for the response. It does seem that the serial number is specific to the version. I have downlaoded and tried Premiere Elements 2021 on my computer and even though it has an older i5 processor and only 6 gb of ram it seems to work for the things I need to do. Now I can purchase the program. Thanks.