Type of Culminating Activity
Master of Science in Mathematics
Jens Harlander, Ph.D.
This paper is concerned with constructing countably many, non-free stably free modules for the Klein bottle group. The work is based on the papers “Stably Free, Projective Right Ideals" by J.T. Stafford (1985) and “Projective, Nonfree Modules Over Group Rings of Solvable Groups" by V. A. Artamonov (1981). Stafford proves general results that guarantee the existence of non-free stably frees for the Klein bottle group but has not made the argument explicit. Artamonov allows us to construct infinitely many non-free stably free modules. This paper will also construct presentations and sets of generators for these modules. This paper concludes with applications for the Klein bottle group and the Homotopy Classification Problem.
Misseldine, Andrew, "Stably Free Modules Over the Klein Bottle" (2010). Boise State University Theses and Dissertations. Paper 106.