FACTORIZATION PROPERTIES OF CONGRUENCE MONOIDS

Arielle Fujiwara1,  Joseph Gibson2,  Matthew Jenssen3,  Daniel Montealegre4,  Vadim Ponomarenko*5,  Ari Tenzer6

Roosevelt University1, Mathematics and Actuarial Science, Chicago, IL 60605
University of Texas at San Antonio2, San Antonio, TX 78249
Queen's College: University of Cambridge3, Cambridge
University of California, Los Angeles4, Los Angeles, CA 90024
San Diego State University5, Math and Statistics, San Diego, CA 92182
Washington University in St. Louis6, St. Louis, MO 63130

vadim@sciences.sdsu.edu

Abstract

Look at the residues of elements of a subset of the natural numbers that form a multiplicatively closed set modulo n and its corresponding congruence monoid (CM). Unlike the naturals, many CMs enjoy the property of non-unique factorization into irreducibles. This opens the door to the study of arithmetic invariants associated with non-unique factorization theory; most important to us will be the concept of elasticity. In particular, we will discuss when a given CM has finite elasticity. Throughout this talk, we explore the arithmetic properties of the CM in terms of the corresponding set of residues.

A. Fujiwara was supported by NSF-REU Grant No. 1061366

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