There are a few states that have laws covering this situation, otherwise it probably depends on the agreements you signed when you were hired.

stackoverflow.com/questions/401269/states-having-nonassignable-invention-exceptions-similar-to-california-code-sect

I don't know what the default is in cases where there's no explicit agreement, but this outcome seems possible.

www.dilbert.com/2009-01-22/

Forgive me that the links aren't clickable, I'm having trouble submitting this comment and I suspect it's a bozo filter that I'm tripping.