First of all, this question must be decided by the adviser, not by the student.
The student must accept any decision if his/her adviser.

Most advisers that I know (mathematicians) will not co-author a paper with a student, if
the contribution of a student is substantial. But this depends on a person of course,
in particular on the adviser's own experience when s/he was a student.

For example, the first paper of Ahlfors was not written by himself (though the main idea was his). As a result, Ahlfors established a rule to never co-author his PhD student paper.
(He mentions this is his comments to his first paper in his Collected papers).

Myself, I try to follow this rule, but exceptions are possible.

When should a supervisor be a co-author?
I am trying to remember the name of a TV show in the late 70s, perhaps early 80s, in which a group of two or three people (there was a man and a woman) travelled between different sections of a large spaceship. The spaceship carried people from Earth. I seem to remember that the various sections of the spaceship (which were semi-spherical) contained different environments, and different ethnicities from Earth. Hence the protagonists found themselves in an unknown situation each time they entered a new part of the ship.

Can anyone help me to find out the name and suggest where I could get a hold of episodes?
