Dr. Nicholas Baeth, University of Central Missouri

Matrices Behaving Badly: Examples of non-unique factorization within matrix semigroups

ABSTRACT: In the perfect world of the positive integers every element can be uniquely factored (up to order) as a product of prime numbers. However, this nice property of "unique factorization" does not hold in every algebraic setting. In this talk we will investigate unique and non-unique factorizations of elements in various categories of integer-valued matrices. Through these examples, we will explore the good, the bad, and the ugly in the world of of factorization theory and introduce several important factorization-theoretic invariants.