# Research

I am interested in the intersection of Ring Theory and Linear Algebra. More specifically, I study algebras which are linearly spanned by elements of various types and their embeddings as infinite matrix algebras. Furthermore, I am interested in in exploring these topics in combinatorially defined algebras such as Leavitt path algebras .

I am also interested in Algebraic Coding Theory, specifically generalizations of Reed-Solomon codes and their applications to problems of communication and distributed storage.

I keep a semi-updated blog of my research activities and other odds and ends here: InOverMyHead Math Blog

**Peer-Reviewed Publications:**

(With S. R. Lopez-Permouth) On the Associativity of Infinite Matrix Multiplication.

*American Mathematical Monthly*. (**arXiv link**).(With S. R. Lopez-Permouth) Algebras Having Bases Consisting Solely of Strongly Regular Elements.

*Journal of Pure and Applied Algebra*.(**preprint****)**(With S. R. Lopez-Permouth) Bases of Leavitt Path Algebras with only Strongly Regular Elements

*.**Communications in Algebra.*(**preprint)**Ideal Extensions and Directly Infinite Algebras.

*Pure and Applied Algebra*. (link)

**Preprints:**

(With D. Herden and A. Pasi) Forcing a Basis into Aleph1 Free Groups.

Ideal Extensions and Directly Infinite Matrix Algebras. (arXiv link)

A Family of Almost Invertible Infinite Matrices. (arXiv link)

**Thesis and Dissertations:**

Dissertation:

*Some Topics in Infinite-Dimensional Algebra*. Ohio University. Under the direction of Sergio R. Lopez-PermouthMasters Thesis:

*On a Generalization of Clean Rings*. Saint Louis University. Under the direction of Ashish K. Srivastava