Fall 2013, Thursdays, Milner 216, 4:00-4:50 PM

Date: October 24

"  Factorization Properties of Congruence Monoids "
 Joseph Gibson  


Take a submonoid of the natural numbers which when reducedmodulo n is multiplicatively closed. This submonoid is known as a 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 elasticy. In particular, we give a complete characterization of when a given CM has finite elasticity. Throughout, we explore the arithmetic properties of the CM in terms of the arithmetic and algebraic properties of its generator.