## Dissertations, Theses, and Student Research Papers in Mathematics

#### Title

A Tensor's Torsion

Roger Wiegand

Tom Marley

8-2018

#### 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

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