#### Date of Graduation

8-2018

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy in Mathematics (PhD)

#### Degree Level

Graduate

#### Department

Mathematical Sciences

#### Advisor

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.

#### Recommended Citation

Jabbar Nezhad, Babak, "Equations of multi-Rees Algebras" (2018). *Theses and Dissertations*. 2900.

https://scholarworks.uark.edu/etd/2900