Anna Lawson

Teaching

University of Tennessee

Calculus I (Math 141)

Fall 2021, Fall 2019, Spring 2019, Fall 2018

Calculus II (Math 142)

Spring 2021, Fall 2020, Spring 2020

Basic Calculus (Math 125)

Spring 2018

College Algebra (Math 119)

Fall 2017

Publications

On Finite Molecularization Domains

We advance an ideal-theoretic analogue of a “finite factorization domain” (FFD), giving such a domain the moniker “finite molecularization domain” (FMD). We characterize FMDs as those factorable domains (termed “molecular domains” in the paper) for which every nonzero ideal is divisible by only finitely many nonfactorable ideals (termed “molecules” in the paper) and the monoid of nonzero ideals of the domain is unit-cancellative, in the language of Fan, Geroldinger, Kainrath, and Tringali. We develop a number of connections, particularly at the local level, amongst the concepts of “FMD”, “FFD”, and the “finite superideal domains” (FSDs) of Hetzel and Lawson. Characterizations of when k[X²,X³], where k is a field, and the classical D+M construction are FMDs are provided. We also demonstrate that if R is a Dedekind domain with the finite norm property, then R[X] is an FMD.

Andrew J. Hetzel. Anna L. Lawson. Andreas Reinhart. "On finite molecularization domains." J. Commut. Algebra 13 (1) 69 - 87, Spring 2021. https://doi.org/10.1216/jca.2021.13.69