I have been taking a course in Homological Algebra and revisiting the lecture notes for some reason. There was a non-answered question about showing two non zero modules A,B over a non trivial unital ring(in fact upper triangular matrices) are projective modules. I won't explain what these modules are because it requires a lot of work.

I thought that if there is a relation between being cyclic and/or simple AND projective then I can use that. However, I couldn't find any such relation.

Is there any relation between cyclic and/or simple modules and projective modules?