A Tensor's Torsion

Authors

Neil Steinburg, University of Nebraska-LincolnFollow

First Advisor

Roger Wiegand

Second Advisor

Tom Marley

Date of this Version

8-2018

Document Type

Article

Comments

A DISSERTATION Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfillment of Requirements For the Degree of Doctor of Philosophy, Major: Mathematics, Under the Supervision of Roger Wiegand and Tom Marley. Lincoln, Nebraska : August, 2018.

Copyright (c) 2018 Neil Steinburg

Abstract

While tensor products are quite prolific in commutative algebra, even some of their most basic properties remain relatively unknown. We explore one of these properties, namely a tensor's torsion. In particular, given any finitely generated modules, M and N over a ring R, the tensor product $M\otimes_R N$ almost always has nonzero torsion unless one of the modules M or N is free. Specifically, we look at which rings guarantee nonzero torsion in tensor products of non-free modules over the ring. We conclude that a specific subclass of one-dimensional Gorenstein rings will have this property.

Adviser: Roger Wiegand and Tom Marley