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Factorization in Some Interesting Integral Domains

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If you have a question about this talk, please contact Anton Evseev.

Let K be a number field and O_K its ring of integers. It is well known that O_K is a unique factorization domain if and only if the ideal class number of O_K is 1. A less well known result of Carlitz (1960), states that for every x in O_K, every factorization of x into irreducibles has the same length if and only if the ideal class number of O_K is at most 2.

In this talk we will focus on three types of domains where unique factorization does not generally hold: Arithmetic Congruence Monoids, Block Monoids and Numerical Monoids. We will define some interesting factorization invariants and look at them in these three settings. We will give many examples and few proofs and will state several unsolved problems, so this talk should be accessible to a wide audience.

This talk is part of the Junior Algebra/Logic/Number Theory seminar series.

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