Publication Date
5-2011
Type of Culminating Activity
Thesis
Degree Title
Master of Science in Mathematics
Department Filter
Mathematics
Department
Mathematics
Supervisory Committee Chair
Jens Harlander, Ph.D.
Abstract
In 1964, Paul Cohn showed that if F is a finitely-generated free group, and Q a field, then all ideals in the group ring Q[F] are free as Q[F]-modules. In particular, all finitely-generated submodules of free Q[F]-modules are free. In 1990, Cynthia Hog-Angeloni reproved this theorem using techniques from geometric group theory. Leaning on Hog-Angeloni's methods, we prove an analogous statement for crossed products D * F, with D a division ring.
With this result in hand, we prove that if G = H⋊F, the semi-direct product of H with F, so that the group ring D[G] may be localized at the sub-group ring k[H]―{0), then the resulting localized group ring also has the property that finitely-generated submodules of free modules are free.
Recommended Citation
Davidson, Nicholas, "Modules Over Localized Group Rings for Groups Mapping Onto Free Groups" (2011). Boise State University Theses and Dissertations. 170.
https://scholarworks.boisestate.edu/td/170
