We study spanning sets for the Kauffman bracket skein module S(M,Q(A)) of orientable Seifert fibered spaces with orientable base and non-empty boundary. As a consequence, we show that the KBSM of such manifolds is a finitely generated S(∂M, Q(A))-module.

This work is the result of a course at and funding from Colby College. The authors are grateful to Puttipong Pongtanapaisan for helpful conversations and Scott Taylor for all his valuable advice. In addition, the authors want to thank the referee for suggesting ideas that improved the results of this work.