Is "unix" supposed to be "unix", "Unix", or "UNIX"?
From the wikipedia article you linked:
trademarked as UNIX
Also from the other article you linked:
The Bell Labs documentation was very careful to always spell UNIX in all capital letters, and small caps whereever possible.
This is a generic name for all UNIX-like operating systems, including Linux. The last patent on unix expired in Septmber 1989, and it became legal to freely distribute a unix that was not derived from UNIX. On that date, unix (the conceptual design and its associated technological cullture) ceased to be the intellectual property of whatever corporation owned the UNIX code base, and became part of the human cultural heritage.