It has been (implicitly) known since the time of Gauss that polynomial rings over factorial domains are factorial. In modern times, Gilmer and Parker extended this result to a characterization of factorial monoid domains. In this talk we will consider the more general topic of commutative monoid rings (possibly with proper zero divisors) that satisfy various notions of "factoriality." To make the presentation accessible to a wide audience, we will include a review of some definitions and basic facts related to monoid rings and factorization theory. This talk is based on research done by the speaker in collaboration with Chris Mooney and Rhys Roberts.
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