## Date of Graduation

8-2018

## Document Type

Dissertation

## Degree Name

Doctor of Philosophy in Mathematics (PhD)

## Degree Level

Graduate

## Department

Mathematical Sciences

## Advisor/Mentor

Mark Johnson

## Committee Member

Paolo Mantero

## Second Committee Member

Lance Miller

## Keywords

Rees Algebra

## Abstract

In this thesis we describe the defining equations of certain multi-Rees algebras. First, we determine the defining equations of the multi-Rees algebra $R[I^{a_1}t_1,\dots,I^{a_r}t_r]$ over a Noetherian ring $R$ when $I$ is an ideal of linear type. This generalizes a result of Ribbe and recent work of Lin-Polini and Sosa. Second, we describe the equations defining the multi-Rees algebra $R[I_1^{a_1}t_1,\dots,I_r^{a_r}t_r]$, where $R$ is a Noetherian ring containing a field and the ideals are generated by a subset of a fixed regular sequence.

## Citation

Jabbar Nezhad, B.
(2018). Equations of multi-Rees Algebras. * Graduate Theses and Dissertations*
Retrieved from https://scholarworks.uark.edu/etd/2900