Mathematics Professor’s Paper Accepted into Journal
Dr. Melissa DiMarco had her paper accepted into the Journal of Pure and Applied Algebra (JPAA)
Dr. Melissa DiMarco had her paper ”The Ext-algebra and associated monomial algebra of a finite dimensional K-algebra” accepted for publication in JPAA. Algebraists, like Dr. DiMarco, study structures that mimic a set of numbers. They also study sets with binary operations, and give these sets names based on which properties are preserved. For example, an algebraist will study sets called groups, rings, fields, vector spaces, modules, and algebras to name a few.
Finding relationships between these structures is a defining goal of abstract algebra. In this paper, Dr. DiMarco studies a structure called a K-algebra A where K is an algebraically closed field. Her paper finds a new relationship between that algebra and its ext-algebra, where the ext-algebra is a well-known algebra associated to the original K-algebra. In particular, she proves that if the AGS resolution of A is minimal and its associated monomial algebra is finitely generated, then the ext-algebra is finitely generated. Dr. DiMarco looks at 2-d-determined algebra as an example, to see that if A is a 2-d determined algebra and if its AGS resolution is minimal, then its ext-algebra is generated in degrees 0,1, and 2.