Did EMC own VMware?

Hello there, I'm curious about a specific aspect of the tech industry's past. Can you clarify for me if EMC, a well-known data storage and cloud computing company, ever owned VMware, the virtualization software giant? It's a bit of a historical question, but I'm fascinated by the mergers and acquisitions that shape the tech landscape. If EMC did own VMware, when did this ownership take place, and what led to the eventual separation, if any? Thanks in advance for shedding some light on this topic.